Space of modular forms of level 4, weight 37, and Character 4.b

• Label: 4.37.b
• Level: $4$
• Weight: $37$
• Character orbit: 4.b
• Rep. character: $\chi_{4}(3,\cdot)$
• Character field: $\Q$
• Dimension: $17$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 37 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{37}(4, [\chi])\).

	Total	New	Old
Modular forms	19	19	0
Cusp forms	17	17	0
Eisenstein series	2	2	0

Trace form

\( 17 q - 84916 q^{2} + 63108769040 q^{4} + 1587598983826 q^{5} - 217628996575488 q^{6} - 6116838281275456 q^{8} - 785089825520546847 q^{9} + O(q^{10}) \)

Decomposition of \(S_{37}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.37.b.a	$4$	$37$	4.b	4.b	$2$	$1$	$1$	$32.837$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-262144\)	\(0\)	\(-42\!\cdots\!34\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{18}q^{2}+2^{36}q^{4}-4228490555534q^{5}+\cdots\)
4.37.b.b	$4$	$37$	4.b	4.b	$2$	$16$	$16$	$32.837$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(177228\)	\(0\)	\(58\!\cdots\!60\)	\(0\)	$2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(11077+\beta _{1})q^{2}+(50+198\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)