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

• Label: 1150.2.e
• Level: $1150$
• Weight: $2$
• Character orbit: 1150.e
• Rep. character: $\chi_{1150}(643,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $360$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(360\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	384	72	312
Cusp forms	336	72	264
Eisenstein series	48	0	48

Trace form

72 * q - 8 * q^3 - 16 * q^6 - 8 * q^12 + 16 * q^13 - 72 * q^16 + 16 * q^18 + 8 * q^23 - 16 * q^26 + 16 * q^27 + 48 * q^31 + 56 * q^36 - 48 * q^41 - 16 * q^46 + 8 * q^47 + 8 * q^48 + 16 * q^52 - 32 * q^62 - 32 * q^71 + 16 * q^72 - 88 * q^73 - 24 * q^77 + 40 * q^78 + 200 * q^81 + 40 * q^82 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 16 * q^96 - 64 * q^98

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.e.a	$1150$	$2$	1150.e	115.e	$4$	$8$	$4$	$9.183$	\(\Q(\zeta_{16})\)	None					230.2.e.c	$4$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_1 q^{2}+(2\beta_{3}-2)q^{3}+\beta_{3} q^{4}+\cdots\)
1150.2.e.b	$1150$	$2$	1150.e	115.e	$4$	$8$	$4$	$9.183$	8.0.110166016.2	None					230.2.e.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}+(1+\beta _{5})q^{3}+\beta _{7}q^{4}+(1-\beta _{4}+\cdots)q^{6}+\cdots\)
1150.2.e.c	$1150$	$2$	1150.e	115.e	$4$	$8$	$4$	$9.183$	8.0.110166016.2	None					230.2.e.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}+(1+\beta _{5})q^{3}+\beta _{7}q^{4}+(1-\beta _{4}+\cdots)q^{6}+\cdots\)
1150.2.e.d	$1150$	$2$	1150.e	115.e	$4$	$16$	$8$	$9.183$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			1150.2.e.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{4}+(-1+\cdots)q^{6}+\cdots\)
1150.2.e.e	$1150$	$2$	1150.e	115.e	$4$	$16$	$8$	$9.183$	16.0.\(\cdots\).1	None		✓			1150.2.e.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(\beta _{10}-\beta _{12})q^{3}-\beta _{9}q^{4}+\cdots\)
1150.2.e.f	$1150$	$2$	1150.e	115.e	$4$	$16$	$8$	$9.183$	16.0.\(\cdots\).1	None		✓			1150.2.e.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+(-\beta _{5}+\beta _{7}+\beta _{11})q^{3}-\beta _{8}q^{4}+\cdots\)

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

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