Space of modular forms of level 828, weight 2, and Character 828.c

• Label: 828.2.c
• Level: $828$
• Weight: $2$
• Character orbit: 828.c
• Rep. character: $\chi_{828}(323,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(11\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(828, [\chi])\).

	Total	New	Old
Modular forms	152	44	108
Cusp forms	136	44	92
Eisenstein series	16	0	16

Trace form

\( 44 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(828, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
828.2.c.a	$828$	$2$	828.c	12.b	$2$	$2$	$2$	$6.612$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}+2\beta q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots\)
828.2.c.b	$828$	$2$	828.c	12.b	$2$	$2$	$2$	$6.612$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2q^{4}+2\beta q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots\)
828.2.c.c	$828$	$2$	828.c	12.b	$2$	$8$	$8$	$6.612$	8.0.18939904.2	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots\)
828.2.c.d	$828$	$2$	828.c	12.b	$2$	$8$	$8$	$6.612$	8.0.18939904.2	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{3})q^{2}+(\beta _{2}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
828.2.c.e	$828$	$2$	828.c	12.b	$2$	$12$	$12$	$6.612$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}+(-\beta _{2}+\beta _{8})q^{4}+(-\beta _{4}+\beta _{6}+\cdots)q^{5}+\cdots\)
828.2.c.f	$828$	$2$	828.c	12.b	$2$	$12$	$12$	$6.612$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(\beta _{2}+\beta _{7})q^{4}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(828, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(828, [\chi]) \cong \)