Space of modular forms of level 5415, weight 2, and trivial character

• Label: 5415.2.a
• Level: $5415$
• Weight: $2$
• Character orbit: 5415.a
• Rep. character: $\chi_{5415}(1,\cdot)$
• Character field: $\Q$
• Dimension: $228$
• Newform subspaces: $46$
• Sturm bound: $1520$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5415.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 46 \)
Sturm bound:			\(1520\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5415))\).

	Total	New	Old
Modular forms	800	228	572
Cusp forms	721	228	493
Eisenstein series	79	0	79

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

\(3\)	\(5\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(27\)
\(+\)	\(+\)	\(-\)	\(-\)	\(30\)
\(+\)	\(-\)	\(+\)	\(-\)	\(35\)
\(+\)	\(-\)	\(-\)	\(+\)	\(21\)
\(-\)	\(+\)	\(+\)	\(-\)	\(30\)
\(-\)	\(+\)	\(-\)	\(+\)	\(27\)
\(-\)	\(-\)	\(+\)	\(+\)	\(22\)
\(-\)	\(-\)	\(-\)	\(-\)	\(36\)
Plus space			\(+\)	\(97\)
Minus space			\(-\)	\(131\)

Trace form

228 * q - 4 * q^2 + 2 * q^3 + 228 * q^4 + 2 * q^6 - 12 * q^8 + 228 * q^9 + 4 * q^10 - 8 * q^11 + 6 * q^12 + 8 * q^13 + 2 * q^15 + 220 * q^16 + 8 * q^17 - 4 * q^18 - 8 * q^20 + 8 * q^21 - 8 * q^22 - 6 * q^24 + 228 * q^25 + 24 * q^26 + 2 * q^27 + 8 * q^28 - 8 * q^29 - 2 * q^30 + 12 * q^32 + 8 * q^34 + 228 * q^36 + 8 * q^37 + 4 * q^39 + 12 * q^40 + 8 * q^41 - 8 * q^42 - 24 * q^43 - 16 * q^44 + 32 * q^46 - 16 * q^47 + 30 * q^48 + 260 * q^49 - 4 * q^50 - 12 * q^51 + 40 * q^52 + 2 * q^54 - 16 * q^55 + 48 * q^56 + 48 * q^58 - 48 * q^59 + 6 * q^60 + 32 * q^61 + 80 * q^62 + 236 * q^64 + 8 * q^65 + 32 * q^66 - 24 * q^67 + 96 * q^68 + 8 * q^69 + 8 * q^70 - 16 * q^71 - 12 * q^72 + 8 * q^73 + 40 * q^74 + 2 * q^75 - 8 * q^77 + 4 * q^78 + 228 * q^81 + 40 * q^82 - 16 * q^83 + 8 * q^84 - 12 * q^87 - 8 * q^88 + 24 * q^89 + 4 * q^90 - 48 * q^91 - 40 * q^92 + 24 * q^93 - 48 * q^94 + 10 * q^96 + 56 * q^97 - 36 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5415))\) 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	19
5415.2.a.a	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				285.2.i.a	$1$	$2$	\(-2\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.b	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				285.2.i.c	$1$	$1$	\(-2\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.c	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				285.2.a.b	$1$	$1$	\(-1\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
5415.2.a.d	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓	✓			5415.2.a.d	$1$	$0$	\(-1\)	\(1\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5415.2.a.e	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				285.2.a.c	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
5415.2.a.f	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				285.2.i.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
5415.2.a.g	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				285.2.i.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
5415.2.a.h	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				285.2.a.a	$1$	$2$	\(1\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
5415.2.a.i	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓	✓			5415.2.a.d	$1$	$1$	\(1\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
5415.2.a.j	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				15.2.a.a	$1$	$0$	\(1\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-3q^{8}+\cdots\)
5415.2.a.k	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				285.2.i.a	$1$	$0$	\(2\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.l	$5415$	$2$	5415.a	1.a	$1$	$1$	$1$	$43.239$	\(\Q\)	None	✓				285.2.i.c	$1$	$1$	\(2\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
5415.2.a.m	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{17}) \)	None	✓	✓			5415.2.a.m	$1$	$1$	\(-2\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.n	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{2}) \)	None	✓				285.2.a.g	$1$	$0$	\(-2\)	\(-2\)	\(-2\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.o	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{2}) \)	None	✓				285.2.i.d	$1$	$1$	\(-2\)	\(2\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.p	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{2}) \)	None	✓				285.2.a.f	$1$	$1$	\(-2\)	\(2\)	\(-2\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.q	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{5}) \)	None	✓				285.2.i.e	$1$	$0$	\(-1\)	\(2\)	\(-2\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
5415.2.a.r	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{3}) \)	None	✓				285.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}+q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.s	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{7}) \)	None	✓				285.2.a.d	$1$	$0$	\(0\)	\(2\)	\(2\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+5q^{4}+q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.t	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{5}) \)	None	✓				285.2.i.e	$1$	$0$	\(1\)	\(-2\)	\(-2\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
5415.2.a.u	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{2}) \)	None	✓				285.2.i.d	$1$	$1$	\(2\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-q^{5}+\cdots\)
5415.2.a.v	$5415$	$2$	5415.a	1.a	$1$	$2$	$2$	$43.239$	\(\Q(\sqrt{17}) \)	None	✓	✓			5415.2.a.m	$1$	$0$	\(2\)	\(2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
5415.2.a.w	$5415$	$2$	5415.a	1.a	$1$	$3$	$3$	$43.239$	3.3.148.1	None	✓	✓			5415.2.a.w	$1$	$1$	\(-1\)	\(3\)	\(3\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5415.2.a.x	$5415$	$2$	5415.a	1.a	$1$	$3$	$3$	$43.239$	3.3.148.1	None	✓	✓			5415.2.a.w	$1$	$0$	\(1\)	\(-3\)	\(3\)	\(-4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
5415.2.a.y	$5415$	$2$	5415.a	1.a	$1$	$5$	$5$	$43.239$	5.5.8797896.1	None	✓				285.2.i.f	$1$	$0$	\(-1\)	\(-5\)	\(5\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.z	$5415$	$2$	5415.a	1.a	$1$	$5$	$5$	$43.239$	5.5.8797896.1	None	✓				285.2.i.f	$1$	$0$	\(1\)	\(5\)	\(5\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.ba	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.966125.1	None	✓	✓			5415.2.a.ba	$1$	$1$	\(-3\)	\(-6\)	\(6\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{2}-q^{3}+(2-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bb	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.1397493.1	None	✓				285.2.u.a	$1$	$1$	\(-3\)	\(6\)	\(6\)	\(-6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{5})q^{2}+q^{3}+(\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bc	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.5061125.1	None	✓	✓			5415.2.a.bc	$1$	$1$	\(-3\)	\(6\)	\(-6\)	\(6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5415.2.a.bd	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.2591125.1	None	✓	✓			5415.2.a.bd	$1$	$1$	\(-1\)	\(-6\)	\(6\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5415.2.a.be	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.5516125.1	None	✓	✓			5415.2.a.be	$1$	$1$	\(-1\)	\(6\)	\(-6\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
5415.2.a.bf	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.5516125.1	None	✓	✓			5415.2.a.be	$1$	$0$	\(1\)	\(-6\)	\(-6\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
5415.2.a.bg	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.2591125.1	None	✓	✓			5415.2.a.bd	$1$	$0$	\(1\)	\(6\)	\(6\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(\beta _{2}-\beta _{3})q^{4}+q^{5}+\cdots\)
5415.2.a.bh	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.1397493.1	None	✓				285.2.u.a	$1$	$1$	\(3\)	\(-6\)	\(6\)	\(-6\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{5})q^{2}-q^{3}+(\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bi	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.5061125.1	None	✓	✓			5415.2.a.bc	$1$	$0$	\(3\)	\(-6\)	\(-6\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
5415.2.a.bj	$5415$	$2$	5415.a	1.a	$1$	$6$	$6$	$43.239$	6.6.966125.1	None	✓	✓			5415.2.a.ba	$1$	$0$	\(3\)	\(6\)	\(6\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{2}+q^{3}+(2-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
5415.2.a.bk	$5415$	$2$	5415.a	1.a	$1$	$9$	$9$	$43.239$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		285.2.u.b	$1$	$1$	\(-3\)	\(9\)	\(-9\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
5415.2.a.bl	$5415$	$2$	5415.a	1.a	$1$	$9$	$9$	$43.239$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				285.2.u.b	$1$	$1$	\(3\)	\(-9\)	\(-9\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
5415.2.a.bm	$5415$	$2$	5415.a	1.a	$1$	$12$	$12$	$43.239$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		5415.2.a.bm	$1$	$1$	\(-4\)	\(-12\)	\(-12\)	\(-10\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{9}q^{2}-q^{3}+(1+\beta _{7}-\beta _{9})q^{4}-q^{5}+\cdots\)
5415.2.a.bn	$5415$	$2$	5415.a	1.a	$1$	$12$	$12$	$43.239$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		5415.2.a.bn	$1$	$1$	\(-4\)	\(12\)	\(12\)	\(-6\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{8}+\beta _{9})q^{4}+q^{5}+\cdots\)
5415.2.a.bo	$5415$	$2$	5415.a	1.a	$1$	$12$	$12$	$43.239$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓		✓		285.2.u.c	$1$	$0$	\(-3\)	\(-12\)	\(-12\)	\(6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.bp	$5415$	$2$	5415.a	1.a	$1$	$12$	$12$	$43.239$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				285.2.u.c	$1$	$0$	\(3\)	\(12\)	\(-12\)	\(6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.bq	$5415$	$2$	5415.a	1.a	$1$	$12$	$12$	$43.239$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			5415.2.a.bn	$1$	$0$	\(4\)	\(-12\)	\(12\)	\(-6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{8}+\beta _{9})q^{4}+q^{5}+\cdots\)
5415.2.a.br	$5415$	$2$	5415.a	1.a	$1$	$12$	$12$	$43.239$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			5415.2.a.bm	$1$	$0$	\(4\)	\(12\)	\(-12\)	\(-10\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{9}q^{2}+q^{3}+(1+\beta _{7}-\beta _{9})q^{4}-q^{5}+\cdots\)
5415.2.a.bs	$5415$	$2$	5415.a	1.a	$1$	$15$	$15$	$43.239$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		285.2.u.d	$1$	$0$	\(-3\)	\(-15\)	\(15\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5415.2.a.bt	$5415$	$2$	5415.a	1.a	$1$	$15$	$15$	$43.239$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓		✓		285.2.u.d	$1$	$0$	\(3\)	\(15\)	\(15\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5415))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5415)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\)\(^{\oplus 2}\)