Space of modular forms of level 1476, weight 2, and Character 1476.d

• Label: 1476.2.d
• Level: $1476$
• Weight: $2$
• Character orbit: 1476.d
• Rep. character: $\chi_{1476}(1475,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $4$
• Sturm bound: $504$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1476.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 492 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(504\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1476, [\chi])\).

	Total	New	Old
Modular forms	260	84	176
Cusp forms	244	84	160
Eisenstein series	16	0	16

Trace form

\( 84 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1476, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1476.2.d.a	$1476$	$2$	1476.d	492.d	$2$	$4$	$4$	$11.786$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{8}^{2}q^{2}-2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{2}q^{8}+\cdots\)
1476.2.d.b	$1476$	$2$	1476.d	492.d	$2$	$8$	$8$	$11.786$	8.0.\(\cdots\).5	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{4})q^{2}+(-1-\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots\)
1476.2.d.c	$1476$	$2$	1476.d	492.d	$2$	$8$	$8$	$11.786$	8.0.\(\cdots\).5	None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(-2+\beta _{4})q^{4}-2\beta _{6}q^{5}+\cdots\)
1476.2.d.d	$1476$	$2$	1476.d	492.d	$2$	$64$	$64$	$11.786$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1476, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1476, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(492, [\chi])\)\(^{\oplus 2}\)