Space of modular forms of level 7605, weight 2, and trivial character

• Label: 7605.2.a
• Level: $7605$
• Weight: $2$
• Character orbit: 7605.a
• Rep. character: $\chi_{7605}(1,\cdot)$
• Character field: $\Q$
• Dimension: $259$
• Newform subspaces: $77$
• Sturm bound: $2184$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7605.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 77 \)
Sturm bound:			\(2184\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7605))\).

	Total	New	Old
Modular forms	1148	259	889
Cusp forms	1037	259	778
Eisenstein series	111	0	111

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(5\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(26\)
\(+\)	\(+\)	\(-\)	\(-\)	\(26\)
\(+\)	\(-\)	\(+\)	\(-\)	\(26\)
\(+\)	\(-\)	\(-\)	\(+\)	\(26\)
\(-\)	\(+\)	\(+\)	\(-\)	\(42\)
\(-\)	\(+\)	\(-\)	\(+\)	\(36\)
\(-\)	\(-\)	\(+\)	\(+\)	\(35\)
\(-\)	\(-\)	\(-\)	\(-\)	\(42\)
Plus space			\(+\)	\(123\)
Minus space			\(-\)	\(136\)

Trace form

259 * q + q^2 + 261 * q^4 - q^5 + 4 * q^7 + 9 * q^8 - 3 * q^10 - 20 * q^14 + 261 * q^16 - 6 * q^17 + 4 * q^19 - 7 * q^20 + 16 * q^22 + 259 * q^25 + 12 * q^28 + 10 * q^29 - 12 * q^31 - 11 * q^32 + 2 * q^34 + 4 * q^35 + 10 * q^37 - 3 * q^40 - 18 * q^41 + 12 * q^43 - 28 * q^44 + 32 * q^46 + 4 * q^47 + 275 * q^49 + q^50 + 10 * q^53 + 4 * q^55 - 40 * q^56 + 6 * q^58 - 4 * q^59 - 22 * q^61 + 241 * q^64 + 24 * q^67 - 6 * q^68 - 8 * q^70 + 16 * q^71 + 14 * q^73 + 22 * q^74 + 48 * q^76 + 20 * q^77 + 12 * q^79 - 15 * q^80 - 42 * q^82 - 32 * q^83 - 10 * q^85 + 76 * q^86 + 52 * q^88 + 2 * q^89 + 20 * q^92 - 60 * q^94 + 12 * q^95 + 18 * q^97 - 31 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7605))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	13
7605.2.a.a	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.i.a	$1$	$1$	\(-2\)	\(0\)	\(1\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}+5q^{7}-2q^{10}+\cdots\)
7605.2.a.b	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				585.2.b.b	$1$	$2$	\(-1\)	\(0\)	\(-1\)	\(-4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.c	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				585.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.d	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.b.b	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.e	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				585.2.b.b	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.f	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				65.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.g	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				15.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-4q^{11}+\cdots\)
7605.2.a.h	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+4q^{11}+\cdots\)
7605.2.a.i	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.b.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}-3q^{7}-3q^{11}+4q^{16}+\cdots\)
7605.2.a.j	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				585.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}+q^{7}+3q^{11}+4q^{16}+\cdots\)
7605.2.a.k	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.i.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-q^{5}+q^{7}+6q^{11}+4q^{16}+\cdots\)
7605.2.a.l	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.i.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-q^{7}-6q^{11}+4q^{16}+\cdots\)
7605.2.a.m	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				585.2.a.e	$1$	$0$	\(0\)	\(0\)	\(1\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+q^{7}-3q^{11}+4q^{16}+\cdots\)
7605.2.a.n	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.b.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}+3q^{7}+3q^{11}+4q^{16}+\cdots\)
7605.2.a.o	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				585.2.b.b	$1$	$1$	\(1\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.p	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.b.b	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.q	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				585.2.a.d	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.r	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				585.2.b.b	$1$	$1$	\(1\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.s	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.i.a	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}-5q^{7}-2q^{10}+\cdots\)
7605.2.a.t	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.a.c	$1$	$0$	\(2\)	\(0\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}+q^{7}-2q^{10}+\cdots\)
7605.2.a.u	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.a.b	$1$	$1$	\(2\)	\(0\)	\(1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
7605.2.a.v	$7605$	$2$	7605.a	1.a	$1$	$1$	$1$	$60.726$	\(\Q\)	None	✓				195.2.a.d	$1$	$1$	\(2\)	\(0\)	\(1\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}+3q^{7}+2q^{10}+\cdots\)
7605.2.a.w	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{13}) \)	None	✓				585.2.b.f	$2$	$1$	\(-4\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+q^{5}-\beta q^{7}-2q^{10}+\cdots\)
7605.2.a.x	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{2}) \)	None	✓				65.2.a.b	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
7605.2.a.y	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{3}) \)	None	✓				195.2.bb.a	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.z	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{3}) \)	None	✓				195.2.i.c	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+\beta q^{7}+\cdots\)
7605.2.a.ba	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{5}) \)	None	✓				65.2.e.a	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(3-2\beta )q^{7}+\cdots\)
7605.2.a.bb	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{13}) \)	None	✓				65.2.e.b	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}-3q^{8}+\cdots\)
7605.2.a.bc	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{17}) \)	None	✓				195.2.b.c	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(-1-\beta )q^{7}+\cdots\)
7605.2.a.bd	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{17}) \)	None	✓				585.2.a.j	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(5\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(3-\beta )q^{7}+\cdots\)
7605.2.a.be	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{3}) \)	None	✓				65.2.a.c	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-q^{5}-2q^{7}-\beta q^{8}-\beta q^{10}+\cdots\)
7605.2.a.bf	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{5}) \)	None	✓				65.2.e.a	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-3+2\beta )q^{7}+\cdots\)
7605.2.a.bg	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{13}) \)	None	✓				65.2.e.b	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}+q^{5}-q^{7}+3q^{8}+\cdots\)
7605.2.a.bh	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{17}) \)	None	✓				195.2.b.c	$1$	$0$	\(1\)	\(0\)	\(2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(1+\beta )q^{7}+\cdots\)
7605.2.a.bi	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{17}) \)	None	✓				585.2.a.j	$1$	$0$	\(1\)	\(0\)	\(2\)	\(5\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(3-\beta )q^{7}+\cdots\)
7605.2.a.bj	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{3}) \)	None	✓				195.2.i.c	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+\beta q^{7}+\cdots\)
7605.2.a.bk	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{3}) \)	None	✓				195.2.bb.a	$1$	$0$	\(2\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+q^{5}+(1-2\beta )q^{7}+\cdots\)
7605.2.a.bl	$7605$	$2$	7605.a	1.a	$1$	$2$	$2$	$60.726$	\(\Q(\sqrt{13}) \)	None	✓				585.2.b.f	$2$	$0$	\(4\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-q^{5}+\beta q^{7}-2q^{10}+\cdots\)
7605.2.a.bm	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.t	$1$	$1$	\(-3\)	\(0\)	\(3\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots\)
7605.2.a.bn	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.u	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
7605.2.a.bo	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.w	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bp	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.x	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(-12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}-4q^{7}+(-1+\cdots)q^{8}+\cdots\)
7605.2.a.bq	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.v	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.br	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				845.2.a.h	$1$	$1$	\(-1\)	\(0\)	\(3\)	\(5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
7605.2.a.bs	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	3.3.564.1	None	✓				65.2.c.a	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1+\beta _{2})q^{7}+\cdots\)
7605.2.a.bt	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	3.3.148.1	None	✓				195.2.i.e	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
7605.2.a.bu	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	3.3.148.1	None	✓				195.2.i.e	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.bv	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	3.3.756.1	None	✓				195.2.i.d	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bw	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	3.3.756.1	None	✓				195.2.i.d	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bx	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	3.3.316.1	None	✓				195.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
7605.2.a.by	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				845.2.a.h	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bz	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.v	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1-\beta _{1})q^{7}+\cdots\)
7605.2.a.ca	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.x	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(12\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+4q^{7}+(1-2\beta _{1}+\cdots)q^{8}+\cdots\)
7605.2.a.cb	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.w	$1$	$0$	\(1\)	\(0\)	\(3\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1})q^{7}+\cdots\)
7605.2.a.cc	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	3.3.564.1	None	✓				65.2.c.a	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
7605.2.a.cd	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.u	$1$	$1$	\(2\)	\(0\)	\(3\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
7605.2.a.ce	$7605$	$2$	7605.a	1.a	$1$	$3$	$3$	$60.726$	\(\Q(\zeta_{14})^+\)	None	✓				2535.2.a.t	$1$	$1$	\(3\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}-q^{5}+\cdots\)
7605.2.a.cf	$7605$	$2$	7605.a	1.a	$1$	$4$	$4$	$60.726$	4.4.4752.1	None	✓				65.2.m.a	$1$	$0$	\(-2\)	\(0\)	\(4\)	\(10\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(3+\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.cg	$7605$	$2$	7605.a	1.a	$1$	$4$	$4$	$60.726$	4.4.7488.1	None	✓				195.2.bb.c	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}-q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.ch	$7605$	$2$	7605.a	1.a	$1$	$4$	$4$	$60.726$	4.4.13824.1	None	✓				195.2.bb.b	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.ci	$7605$	$2$	7605.a	1.a	$1$	$4$	$4$	$60.726$	4.4.13824.1	None	✓				195.2.bb.b	$1$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.cj	$7605$	$2$	7605.a	1.a	$1$	$4$	$4$	$60.726$	4.4.4752.1	None	✓				65.2.m.a	$1$	$1$	\(2\)	\(0\)	\(-4\)	\(-10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots\)
7605.2.a.ck	$7605$	$2$	7605.a	1.a	$1$	$4$	$4$	$60.726$	4.4.7488.1	None	✓				195.2.bb.c	$1$	$0$	\(2\)	\(0\)	\(4\)	\(-6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.cl	$7605$	$2$	7605.a	1.a	$1$	$5$	$5$	$60.726$	5.5.3352656.1	None	✓				585.2.j.h	$1$	$1$	\(-2\)	\(0\)	\(-5\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots\)
7605.2.a.cm	$7605$	$2$	7605.a	1.a	$1$	$5$	$5$	$60.726$	5.5.3352656.1	None	✓				585.2.j.h	$1$	$1$	\(-2\)	\(0\)	\(-5\)	\(1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{4}q^{7}+\cdots\)
7605.2.a.cn	$7605$	$2$	7605.a	1.a	$1$	$5$	$5$	$60.726$	5.5.3352656.1	None	✓				585.2.j.h	$1$	$0$	\(2\)	\(0\)	\(5\)	\(-1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{4}q^{7}+\cdots\)
7605.2.a.co	$7605$	$2$	7605.a	1.a	$1$	$5$	$5$	$60.726$	5.5.3352656.1	None	✓				585.2.j.h	$1$	$0$	\(2\)	\(0\)	\(5\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots\)
7605.2.a.cp	$7605$	$2$	7605.a	1.a	$1$	$9$	$9$	$60.726$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				845.2.a.n	$1$	$0$	\(-3\)	\(0\)	\(-9\)	\(7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7605.2.a.cq	$7605$	$2$	7605.a	1.a	$1$	$9$	$9$	$60.726$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				2535.2.a.bm	$1$	$0$	\(0\)	\(0\)	\(-9\)	\(-10\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
7605.2.a.cr	$7605$	$2$	7605.a	1.a	$1$	$9$	$9$	$60.726$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				2535.2.a.bm	$1$	$0$	\(0\)	\(0\)	\(9\)	\(10\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
7605.2.a.cs	$7605$	$2$	7605.a	1.a	$1$	$9$	$9$	$60.726$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				845.2.a.n	$1$	$0$	\(3\)	\(0\)	\(9\)	\(-7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7605.2.a.ct	$7605$	$2$	7605.a	1.a	$1$	$10$	$10$	$60.726$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				585.2.bu.e	$2$	$1$	\(-4\)	\(0\)	\(10\)	\(0\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{2}+(1+\beta _{5})q^{4}+q^{5}+\beta _{9}q^{7}+\cdots\)
7605.2.a.cu	$7605$	$2$	7605.a	1.a	$1$	$10$	$10$	$60.726$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				585.2.bu.e	$2$	$0$	\(4\)	\(0\)	\(-10\)	\(0\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+(1+\beta _{5})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots\)
7605.2.a.cv	$7605$	$2$	7605.a	1.a	$1$	$12$	$12$	$60.726$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		7605.2.a.cv	$1$	$1$	\(-1\)	\(0\)	\(12\)	\(-12\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.cw	$7605$	$2$	7605.a	1.a	$1$	$12$	$12$	$60.726$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		7605.2.a.cv	$1$	$0$	\(-1\)	\(0\)	\(12\)	\(12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)
7605.2.a.cx	$7605$	$2$	7605.a	1.a	$1$	$12$	$12$	$60.726$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		7605.2.a.cv	$1$	$0$	\(1\)	\(0\)	\(-12\)	\(-12\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.cy	$7605$	$2$	7605.a	1.a	$1$	$12$	$12$	$60.726$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		7605.2.a.cv	$1$	$1$	\(1\)	\(0\)	\(-12\)	\(12\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7605))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7605)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1521))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2535))\)\(^{\oplus 2}\)