Space of modular forms of level 7581, weight 2, and trivial character

• Label: 7581.2.a
• Level: $7581$
• Weight: $2$
• Character orbit: 7581.a
• Rep. character: $\chi_{7581}(1,\cdot)$
• Character field: $\Q$
• Dimension: $340$
• Newform subspaces: $48$
• Sturm bound: $2026$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 7581 = 3 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7581.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 48 \)
Sturm bound:			\(2026\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7581))\).

	Total	New	Old
Modular forms	1052	340	712
Cusp forms	973	340	633
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.

\(3\)	\(7\)	\(19\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(123\)	\(41\)	\(82\)		\(114\)	\(41\)	\(73\)		\(9\)	\(0\)	\(9\)
\(+\)	\(+\)	\(-\)	\(-\)		\(138\)	\(45\)	\(93\)		\(128\)	\(45\)	\(83\)		\(10\)	\(0\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)		\(133\)	\(39\)	\(94\)		\(123\)	\(39\)	\(84\)		\(10\)	\(0\)	\(10\)
\(+\)	\(-\)	\(-\)	\(+\)		\(130\)	\(45\)	\(85\)		\(120\)	\(45\)	\(75\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(+\)	\(-\)		\(140\)	\(49\)	\(91\)		\(130\)	\(49\)	\(81\)		\(10\)	\(0\)	\(10\)
\(-\)	\(+\)	\(-\)	\(+\)		\(125\)	\(36\)	\(89\)		\(115\)	\(36\)	\(79\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(+\)	\(+\)		\(130\)	\(31\)	\(99\)		\(120\)	\(31\)	\(89\)		\(10\)	\(0\)	\(10\)
\(-\)	\(-\)	\(-\)	\(-\)		\(133\)	\(54\)	\(79\)		\(123\)	\(54\)	\(69\)		\(10\)	\(0\)	\(10\)
Plus space			\(+\)		\(508\)	\(153\)	\(355\)		\(469\)	\(153\)	\(316\)		\(39\)	\(0\)	\(39\)
Minus space			\(-\)		\(544\)	\(187\)	\(357\)		\(504\)	\(187\)	\(317\)		\(40\)	\(0\)	\(40\)

Trace form

340 * q - 4 * q^2 + 340 * q^4 - 8 * q^5 + 4 * q^6 - 2 * q^7 - 12 * q^8 + 340 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 2 * q^14 + 8 * q^15 + 332 * q^16 - 16 * q^17 - 4 * q^18 + 2 * q^21 + 16 * q^22 + 8 * q^23 + 12 * q^24 + 332 * q^25 + 16 * q^26 - 6 * q^28 - 16 * q^29 - 8 * q^30 + 12 * q^32 + 8 * q^34 + 4 * q^35 + 340 * q^36 - 8 * q^37 - 16 * q^39 + 24 * q^40 - 24 * q^41 - 2 * q^42 - 32 * q^43 + 8 * q^44 - 8 * q^45 + 16 * q^46 + 8 * q^47 + 340 * q^49 + 36 * q^50 + 8 * q^51 + 8 * q^52 + 4 * q^54 + 32 * q^55 - 18 * q^56 + 56 * q^58 - 16 * q^59 + 40 * q^60 + 80 * q^62 - 2 * q^63 + 348 * q^64 - 32 * q^65 + 8 * q^66 + 16 * q^67 + 16 * q^68 + 16 * q^69 + 20 * q^70 + 40 * q^71 - 12 * q^72 - 16 * q^73 + 48 * q^74 - 16 * q^75 + 32 * q^78 + 96 * q^80 + 340 * q^81 + 104 * q^82 + 64 * q^83 + 6 * q^84 + 32 * q^85 + 64 * q^86 + 16 * q^87 + 96 * q^88 - 24 * q^89 - 8 * q^90 + 4 * q^91 + 112 * q^92 + 8 * q^93 + 48 * q^94 + 68 * q^96 + 8 * q^97 - 4 * q^98 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7581))\) 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	7	19
7581.2.a.a	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	\(\Q\)	None	✓	✓			7581.2.a.a	$1$	$2$	\(-1\)	\(1\)	\(-4\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
7581.2.a.b	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	\(\Q\)	None	✓				399.2.a.c	$1$	$1$	\(-1\)	\(1\)	\(0\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
7581.2.a.c	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	\(\Q\)	None	✓	✓			7581.2.a.a	$1$	$1$	\(1\)	\(-1\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
7581.2.a.d	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	\(\Q\)	None	✓				21.2.a.a	$1$	$0$	\(1\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
7581.2.a.e	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	\(\Q\)	None	✓				399.2.a.b	$1$	$0$	\(1\)	\(-1\)	\(4\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
7581.2.a.f	$7581$	$2$	7581.a	1.a	$1$	$1$	$1$	$60.535$	\(\Q\)	None	✓				399.2.a.a	$1$	$0$	\(1\)	\(1\)	\(0\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{6}+q^{7}-3q^{8}+\cdots\)
7581.2.a.g	$7581$	$2$	7581.a	1.a	$1$	$2$	$2$	$60.535$	\(\Q(\sqrt{5}) \)	None	✓	✓			7581.2.a.g	$1$	$1$	\(-2\)	\(2\)	\(3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
7581.2.a.h	$7581$	$2$	7581.a	1.a	$1$	$2$	$2$	$60.535$	\(\Q(\sqrt{5}) \)	None	✓	✓			7581.2.a.h	$1$	$1$	\(-1\)	\(2\)	\(-4\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-3+2\beta )q^{5}+\cdots\)
7581.2.a.i	$7581$	$2$	7581.a	1.a	$1$	$2$	$2$	$60.535$	\(\Q(\sqrt{5}) \)	None	✓	✓			7581.2.a.h	$1$	$0$	\(1\)	\(-2\)	\(-4\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-3+2\beta )q^{5}+\cdots\)
7581.2.a.j	$7581$	$2$	7581.a	1.a	$1$	$2$	$2$	$60.535$	\(\Q(\sqrt{5}) \)	None	✓	✓			7581.2.a.g	$1$	$0$	\(2\)	\(-2\)	\(3\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+(2-\beta )q^{5}-q^{6}+\cdots\)
7581.2.a.k	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	\(\Q(\zeta_{18})^+\)	None	✓				399.2.bo.a	$1$	$1$	\(-3\)	\(3\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
7581.2.a.l	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	3.3.404.1	None	✓				399.2.a.e	$1$	$0$	\(-1\)	\(-3\)	\(0\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
7581.2.a.m	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	3.3.148.1	None	✓	✓			7581.2.a.m	$1$	$1$	\(-1\)	\(3\)	\(2\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
7581.2.a.n	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	3.3.148.1	None	✓				399.2.a.d	$1$	$1$	\(-1\)	\(3\)	\(4\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
7581.2.a.o	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	3.3.148.1	None	✓	✓			7581.2.a.m	$1$	$0$	\(1\)	\(-3\)	\(2\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
7581.2.a.p	$7581$	$2$	7581.a	1.a	$1$	$3$	$3$	$60.535$	\(\Q(\zeta_{18})^+\)	None	✓				399.2.bo.a	$1$	$1$	\(3\)	\(-3\)	\(0\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+(2\beta _{1}-\beta _{2})q^{5}-q^{6}+\cdots\)
7581.2.a.q	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.6224.1	None	✓	✓			7581.2.a.q	$1$	$1$	\(-2\)	\(-4\)	\(6\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{2}-q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
7581.2.a.r	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.1957.1	None	✓				399.2.k.b	$1$	$1$	\(-1\)	\(-4\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}-q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.s	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.12197.1	None	✓				399.2.k.a	$1$	$1$	\(-1\)	\(-4\)	\(-2\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.t	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.1957.1	None	✓				399.2.k.b	$1$	$1$	\(1\)	\(4\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.u	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.12197.1	None	✓				399.2.k.a	$1$	$1$	\(1\)	\(4\)	\(-2\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.v	$7581$	$2$	7581.a	1.a	$1$	$4$	$4$	$60.535$	4.4.6224.1	None	✓	✓			7581.2.a.q	$1$	$0$	\(2\)	\(4\)	\(6\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
7581.2.a.w	$7581$	$2$	7581.a	1.a	$1$	$5$	$5$	$60.535$	5.5.368464.1	None	✓				399.2.a.g	$1$	$0$	\(-3\)	\(5\)	\(4\)	\(5\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
7581.2.a.x	$7581$	$2$	7581.a	1.a	$1$	$5$	$5$	$60.535$	5.5.1240016.1	None	✓				399.2.a.f	$1$	$1$	\(-1\)	\(-5\)	\(-2\)	\(5\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{2}-q^{3}+(1+\beta _{4})q^{4}+\beta _{2}q^{5}+\cdots\)
7581.2.a.y	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.5953625.1	None	✓	✓			7581.2.a.y	$1$	$1$	\(-3\)	\(6\)	\(2\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{2}+q^{3}+(2-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
7581.2.a.z	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.8512625.1	None	✓	✓			7581.2.a.z	$1$	$0$	\(-2\)	\(-6\)	\(-5\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.ba	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.343395288.1	None	✓				399.2.k.c	$1$	$0$	\(-1\)	\(-6\)	\(0\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
7581.2.a.bb	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.130040728.1	None	✓				399.2.k.d	$1$	$0$	\(-1\)	\(-6\)	\(4\)	\(6\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots\)
7581.2.a.bc	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.343395288.1	None	✓				399.2.k.c	$1$	$0$	\(1\)	\(6\)	\(0\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
7581.2.a.bd	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.130040728.1	None	✓				399.2.k.d	$1$	$0$	\(1\)	\(6\)	\(4\)	\(6\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{5})q^{5}+\cdots\)
7581.2.a.be	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.8512625.1	None	✓	✓			7581.2.a.z	$1$	$1$	\(2\)	\(6\)	\(-5\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{3}+\beta _{4})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7581.2.a.bf	$7581$	$2$	7581.a	1.a	$1$	$6$	$6$	$60.535$	6.6.5953625.1	None	✓	✓			7581.2.a.y	$1$	$0$	\(3\)	\(-6\)	\(2\)	\(-6\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{2}-q^{3}+(2-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
7581.2.a.bg	$7581$	$2$	7581.a	1.a	$1$	$9$	$9$	$60.535$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓				399.2.bo.b	$1$	$1$	\(-3\)	\(-9\)	\(0\)	\(-9\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1-\beta _{5}-\beta _{7}+\beta _{8})q^{4}+\cdots\)
7581.2.a.bh	$7581$	$2$	7581.a	1.a	$1$	$9$	$9$	$60.535$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓		✓		399.2.bo.b	$1$	$1$	\(3\)	\(9\)	\(0\)	\(-9\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1-\beta _{5}-\beta _{7}+\beta _{8})q^{4}+\cdots\)
7581.2.a.bi	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7581.2.a.bi	$1$	$1$	\(-4\)	\(12\)	\(-2\)	\(12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
7581.2.a.bj	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7581.2.a.bj	$1$	$1$	\(-3\)	\(-12\)	\(-2\)	\(12\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
7581.2.a.bk	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7581.2.a.bk	$1$	$1$	\(-1\)	\(-12\)	\(-2\)	\(12\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
7581.2.a.bl	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				399.2.bo.c	$1$	$1$	\(0\)	\(-12\)	\(-12\)	\(12\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots\)
7581.2.a.bm	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓				399.2.bo.c	$1$	$1$	\(0\)	\(12\)	\(-12\)	\(12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{4}+\cdots)q^{5}+\cdots\)
7581.2.a.bn	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7581.2.a.bk	$1$	$0$	\(1\)	\(12\)	\(-2\)	\(12\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
7581.2.a.bo	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7581.2.a.bj	$1$	$0$	\(3\)	\(12\)	\(-2\)	\(12\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
7581.2.a.bp	$7581$	$2$	7581.a	1.a	$1$	$12$	$12$	$60.535$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓			7581.2.a.bi	$1$	$0$	\(4\)	\(-12\)	\(-2\)	\(12\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
7581.2.a.bq	$7581$	$2$	7581.a	1.a	$1$	$18$	$18$	$60.535$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		399.2.bo.e	$1$	$0$	\(0\)	\(-18\)	\(0\)	\(-18\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)
7581.2.a.br	$7581$	$2$	7581.a	1.a	$1$	$18$	$18$	$60.535$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		399.2.bo.d	$1$	$0$	\(0\)	\(-18\)	\(12\)	\(18\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{9}+\cdots)q^{5}+\cdots\)
7581.2.a.bs	$7581$	$2$	7581.a	1.a	$1$	$18$	$18$	$60.535$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓				399.2.bo.e	$1$	$0$	\(0\)	\(18\)	\(0\)	\(-18\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{12}q^{5}+\cdots\)
7581.2.a.bt	$7581$	$2$	7581.a	1.a	$1$	$18$	$18$	$60.535$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓		✓		399.2.bo.d	$1$	$0$	\(0\)	\(18\)	\(12\)	\(18\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{9}+\cdots)q^{5}+\cdots\)
7581.2.a.bu	$7581$	$2$	7581.a	1.a	$1$	$20$	$20$	$60.535$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓		7581.2.a.bu	$1$	$1$	\(-4\)	\(-20\)	\(-2\)	\(-20\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)
7581.2.a.bv	$7581$	$2$	7581.a	1.a	$1$	$20$	$20$	$60.535$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	✓	✓		7581.2.a.bu	$1$	$0$	\(4\)	\(20\)	\(-2\)	\(-20\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7581))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7581)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1083))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2527))\)\(^{\oplus 2}\)