Space of modular forms of level 370, weight 2, and Character 370.b

• Label: 370.2.b
• Level: $370$
• Weight: $2$
• Character orbit: 370.b
• Rep. character: $\chi_{370}(149,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $4$
• Sturm bound: $114$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(114\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(370, [\chi])\).

	Total	New	Old
Modular forms	62	18	44
Cusp forms	54	18	36
Eisenstein series	8	0	8

Trace form

18 * q - 18 * q^4 - 4 * q^5 - 6 * q^9 - 4 * q^10 - 4 * q^14 + 18 * q^16 - 20 * q^19 + 4 * q^20 + 8 * q^21 + 16 * q^25 - 16 * q^29 + 20 * q^30 + 8 * q^31 + 16 * q^35 + 6 * q^36 - 40 * q^39 + 4 * q^40 - 4 * q^41 + 20 * q^45 - 12 * q^46 - 54 * q^49 + 8 * q^50 + 8 * q^51 + 36 * q^55 + 4 * q^56 + 20 * q^59 - 18 * q^64 - 8 * q^66 - 80 * q^69 + 24 * q^71 - 10 * q^74 + 50 * q^75 + 20 * q^76 - 48 * q^79 - 4 * q^80 - 14 * q^81 - 8 * q^84 + 36 * q^85 - 4 * q^86 - 60 * q^89 + 50 * q^90 + 48 * q^91 - 36 * q^94 + 36 * q^95 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(370, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
370.2.b.a	$370$	$2$	370.b	5.b	$2$	$2$	$2$	$2.954$	\(\Q(\sqrt{-1}) \)	None		✓			370.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(-i-2)q^{5}-2 i q^{7}+\cdots\)
370.2.b.b	$370$	$2$	370.b	5.b	$2$	$2$	$2$	$2.954$	\(\Q(\sqrt{-1}) \)	None		✓			370.2.b.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(2 i+1)q^{5}+i q^{7}+\cdots\)
370.2.b.c	$370$	$2$	370.b	5.b	$2$	$4$	$4$	$2.954$	\(\Q(i, \sqrt{6})\)	None		✓			370.2.b.c	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
370.2.b.d	$370$	$2$	370.b	5.b	$2$	$10$	$10$	$2.954$	10.0.\(\cdots\).1	None		✓	✓		370.2.b.d	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{4}-\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(370, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(370, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)