Space of modular forms of level 676, weight 2, and Character 676.h

• Label: 676.2.h
• Level: $676$
• Weight: $2$
• Character orbit: 676.h
• Rep. character: $\chi_{676}(361,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $26$
• Newform subspaces: $5$
• Sturm bound: $182$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(182\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(676, [\chi])\).

	Total	New	Old
Modular forms	224	26	198
Cusp forms	140	26	114
Eisenstein series	84	0	84

Trace form

\( 26 q - q^{3} + 3 q^{7} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(676, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
676.2.h.a	$676$	$2$	676.h	13.e	$6$	$2$	$1$	$5.398$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)
676.2.h.b	$676$	$2$	676.h	13.e	$6$	$4$	$2$	$5.398$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-3+3\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)
676.2.h.c	$676$	$2$	676.h	13.e	$6$	$4$	$2$	$5.398$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{3}q^{5}-\zeta_{12}q^{7}+(3-3\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
676.2.h.d	$676$	$2$	676.h	13.e	$6$	$4$	$2$	$5.398$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-2\zeta_{12}^{2})q^{3}+3\zeta_{12}^{3}q^{5}+(-4\zeta_{12}+\cdots)q^{7}+\cdots\)
676.2.h.e	$676$	$2$	676.h	13.e	$6$	$12$	$6$	$5.398$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{4}-\beta _{7}+2\beta _{9})q^{3}+(-3\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(676, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(676, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)