Space of modular forms of level 1150, weight 4, and Character 1150.b

• Label: 1150.4.b
• Level: $1150$
• Weight: $4$
• Character orbit: 1150.b
• Rep. character: $\chi_{1150}(599,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $19$
• Sturm bound: $720$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1150.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(720\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1150, [\chi])\).

	Total	New	Old
Modular forms	552	100	452
Cusp forms	528	100	428
Eisenstein series	24	0	24

Trace form

100 * q - 400 * q^4 + 24 * q^6 - 808 * q^9 - 32 * q^11 + 1600 * q^16 - 144 * q^19 + 448 * q^21 - 96 * q^24 + 384 * q^26 - 944 * q^29 - 872 * q^31 + 680 * q^34 + 3232 * q^36 - 1168 * q^39 + 756 * q^41 + 128 * q^44 + 184 * q^46 - 4564 * q^49 + 2524 * q^51 - 216 * q^54 - 2296 * q^59 - 932 * q^61 - 6400 * q^64 - 1064 * q^66 - 552 * q^69 - 1576 * q^71 + 2616 * q^74 + 576 * q^76 + 4600 * q^79 + 11060 * q^81 - 1792 * q^84 - 2360 * q^86 + 6764 * q^89 - 6600 * q^91 - 480 * q^94 + 384 * q^96 - 3140 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1150, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1150.4.b.a	$1150$	$4$	1150.b	5.b	$2$	$2$	$2$	$67.852$	\(\Q(\sqrt{-1}) \)	None					46.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+9 i q^{3}-4 q^{4}-18 q^{6}+\cdots\)
1150.4.b.b	$1150$	$4$	1150.b	5.b	$2$	$2$	$2$	$67.852$	\(\Q(\sqrt{-1}) \)	None					230.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+7 i q^{3}-4 q^{4}-14 q^{6}+\cdots\)
1150.4.b.c	$1150$	$4$	1150.b	5.b	$2$	$2$	$2$	$67.852$	\(\Q(\sqrt{-1}) \)	None					230.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+4 i q^{3}-4 q^{4}-8 q^{6}+\cdots\)
1150.4.b.d	$1150$	$4$	1150.b	5.b	$2$	$2$	$2$	$67.852$	\(\Q(\sqrt{-1}) \)	None					230.4.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-4 q^{4}-2 q^{6}-32 i q^{7}+\cdots\)
1150.4.b.e	$1150$	$4$	1150.b	5.b	$2$	$2$	$2$	$67.852$	\(\Q(\sqrt{-1}) \)	None					46.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 i q^{2}+i q^{3}-4 q^{4}+2 q^{6}-12 i q^{7}+\cdots\)
1150.4.b.f	$1150$	$4$	1150.b	5.b	$2$	$2$	$2$	$67.852$	\(\Q(\sqrt{-1}) \)	None					230.4.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 i q^{2}+i q^{3}-4 q^{4}+2 q^{6}+18 i q^{7}+\cdots\)
1150.4.b.g	$1150$	$4$	1150.b	5.b	$2$	$2$	$2$	$67.852$	\(\Q(\sqrt{-1}) \)	None		✓			1150.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 i q^{2}+2 i q^{3}-4 q^{4}+4 q^{6}+\cdots\)
1150.4.b.h	$1150$	$4$	1150.b	5.b	$2$	$2$	$2$	$67.852$	\(\Q(\sqrt{-1}) \)	None					230.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 i q^{2}+5 i q^{3}-4 q^{4}+10 q^{6}+\cdots\)
1150.4.b.i	$1150$	$4$	1150.b	5.b	$2$	$4$	$4$	$67.852$	\(\Q(i, \sqrt{41})\)	None					46.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{2}q^{2}+(-3\beta _{1}-\beta _{2})q^{3}-4q^{4}+\cdots\)
1150.4.b.j	$1150$	$4$	1150.b	5.b	$2$	$4$	$4$	$67.852$	\(\Q(i, \sqrt{73})\)	None					46.4.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(4+\cdots)q^{6}+\cdots\)
1150.4.b.k	$1150$	$4$	1150.b	5.b	$2$	$4$	$4$	$67.852$	\(\Q(i, \sqrt{73})\)	None					230.4.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(4+\cdots)q^{6}+\cdots\)
1150.4.b.l	$1150$	$4$	1150.b	5.b	$2$	$6$	$6$	$67.852$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					230.4.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+\beta _{1}q^{3}-4q^{4}-2\beta _{3}q^{6}+\cdots\)
1150.4.b.m	$1150$	$4$	1150.b	5.b	$2$	$8$	$8$	$67.852$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					230.4.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots\)
1150.4.b.n	$1150$	$4$	1150.b	5.b	$2$	$8$	$8$	$67.852$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					230.4.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots\)
1150.4.b.o	$1150$	$4$	1150.b	5.b	$2$	$8$	$8$	$67.852$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					230.4.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{6}q^{2}+(\beta _{1}-3\beta _{6})q^{3}-4q^{4}+(6+\cdots)q^{6}+\cdots\)
1150.4.b.p	$1150$	$4$	1150.b	5.b	$2$	$10$	$10$	$67.852$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1150.4.a.s	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{5}q^{2}+(-2\beta _{5}+\beta _{8})q^{3}-4q^{4}+\cdots\)
1150.4.b.q	$1150$	$4$	1150.b	5.b	$2$	$10$	$10$	$67.852$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1150.4.a.r	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{6}q^{2}+\beta _{1}q^{3}-4q^{4}+2\beta _{2}q^{6}+\cdots\)
1150.4.b.r	$1150$	$4$	1150.b	5.b	$2$	$10$	$10$	$67.852$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			1150.4.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-4q^{4}+(2+\cdots)q^{6}+\cdots\)
1150.4.b.s	$1150$	$4$	1150.b	5.b	$2$	$12$	$12$	$67.852$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		1150.4.a.w	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta _{7}q^{2}+(\beta _{1}+\beta _{7})q^{3}-4q^{4}+(-2+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1150, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1150, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)