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

• Label: 370.2.bd
• Level: $370$
• Weight: $2$
• Character orbit: 370.bd
• Rep. character: $\chi_{370}(13,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $228$
• Newform subspaces: $2$
• Sturm bound: $114$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.bd (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(114\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	732	228	504
Cusp forms	636	228	408
Eisenstein series	96	0	96

Trace form

\( 228 q + 12 q^{3} + O(q^{10}) \)

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.bd.a	$370$	$2$	370.bd	185.ac	$36$	$108$	$9$	$2.954$		None		✓			370.2.ba.a	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
370.2.bd.b	$370$	$2$	370.bd	185.ac	$36$	$120$	$10$	$2.954$		None		✓	✓		370.2.ba.b	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

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

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