Space of modular forms of level 1150, weight 2, and Character 1150.b

• Label: 1150.2.b
• Level: $1150$
• Weight: $2$
• Character orbit: 1150.b
• Rep. character: $\chi_{1150}(599,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $10$
• Sturm bound: $360$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(360\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1150, [\chi])\).

	Total	New	Old
Modular forms	192	32	160
Cusp forms	168	32	136
Eisenstein series	24	0	24

Trace form

32 * q - 32 * q^4 - 4 * q^6 - 44 * q^9 + 16 * q^11 + 32 * q^16 + 8 * q^19 - 16 * q^21 + 4 * q^24 - 24 * q^26 - 8 * q^31 + 20 * q^34 + 44 * q^36 + 16 * q^39 - 44 * q^41 - 16 * q^44 - 4 * q^46 - 16 * q^49 - 44 * q^51 + 52 * q^54 + 40 * q^59 - 60 * q^61 - 32 * q^64 - 44 * q^66 + 8 * q^69 - 24 * q^71 + 12 * q^74 - 8 * q^76 - 24 * q^79 + 48 * q^81 + 16 * q^84 + 20 * q^86 + 60 * q^89 + 8 * q^91 + 16 * q^94 - 4 * q^96 - 68 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1150, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1150.2.b.a	$1150$	$2$	1150.b	5.b	$2$	$2$	$2$	$9.183$	\(\Q(\sqrt{-1}) \)	None		✓			1150.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+3 i q^{3}-q^{4}-3 q^{6}-4 i q^{7}+\cdots\)
1150.2.b.b	$1150$	$2$	1150.b	5.b	$2$	$2$	$2$	$9.183$	\(\Q(\sqrt{-1}) \)	None		✓			1150.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}-i q^{7}+\cdots\)
1150.2.b.c	$1150$	$2$	1150.b	5.b	$2$	$2$	$2$	$9.183$	\(\Q(\sqrt{-1}) \)	None		✓			1150.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+i q^{7}+i q^{8}+3 q^{9}+\cdots\)
1150.2.b.d	$1150$	$2$	1150.b	5.b	$2$	$2$	$2$	$9.183$	\(\Q(\sqrt{-1}) \)	None					46.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}-4 i q^{7}+i q^{8}+3 q^{9}+\cdots\)
1150.2.b.e	$1150$	$2$	1150.b	5.b	$2$	$2$	$2$	$9.183$	\(\Q(\sqrt{-1}) \)	None		✓			1150.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}-i q^{7}+\cdots\)
1150.2.b.f	$1150$	$2$	1150.b	5.b	$2$	$4$	$4$	$9.183$	\(\Q(i, \sqrt{13})\)	None					230.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
1150.2.b.g	$1150$	$2$	1150.b	5.b	$2$	$4$	$4$	$9.183$	\(\Q(i, \sqrt{21})\)	None					230.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
1150.2.b.h	$1150$	$2$	1150.b	5.b	$2$	$4$	$4$	$9.183$	\(\Q(i, \sqrt{17})\)	None		✓			1150.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(1-\beta _{3})q^{6}+\cdots\)
1150.2.b.i	$1150$	$2$	1150.b	5.b	$2$	$4$	$4$	$9.183$	\(\Q(i, \sqrt{5})\)	None					230.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1150.2.b.j	$1150$	$2$	1150.b	5.b	$2$	$6$	$6$	$9.183$	6.0.77580864.1	None			✓		230.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1150, [\chi])\) into lower level spaces

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