Space of modular forms of level 836, weight 2, and Character 836.b

• Label: 836.2.b
• Level: $836$
• Weight: $2$
• Character orbit: 836.b
• Rep. character: $\chi_{836}(417,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 836 = 2^{2} \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	836.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 209 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(836, [\chi])\).

	Total	New	Old
Modular forms	126	20	106
Cusp forms	114	20	94
Eisenstein series	12	0	12

Trace form

\( 20 q + 2 q^{5} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(836, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
836.2.b.a	$836$	$2$	836.b	209.d	$2$	$4$	$4$	$6.675$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
836.2.b.b	$836$	$2$	836.b	209.d	$2$	$16$	$16$	$6.675$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{3}-\beta _{2}q^{5}+(-\beta _{9}+\beta _{12})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(836, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(836, [\chi]) \cong \)