Space of modular forms of level 3136, weight 2, and Character 3136.e

• Label: 3136.2.e
• Level: $3136$
• Weight: $2$
• Character orbit: 3136.e
• Rep. character: $\chi_{3136}(1567,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $6$
• Sturm bound: $896$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3136 = 2^{6} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3136.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(896\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3136, [\chi])\).

	Total	New	Old
Modular forms	496	80	416
Cusp forms	400	80	320
Eisenstein series	96	0	96

Trace form

\( 80 q - 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3136, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3136.2.e.a	$3136$	$2$	3136.e	56.e	$2$	$8$	$8$	$25.041$	8.0.12960000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{1}q^{5}-2q^{9}+\beta _{7}q^{11}+\cdots\)
3136.2.e.b	$3136$	$2$	3136.e	56.e	$2$	$8$	$8$	$25.041$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}^{2}q^{3}-\zeta_{16}^{7}q^{5}+(1-\zeta_{16}^{4}+\cdots)q^{9}+\cdots\)
3136.2.e.c	$3136$	$2$	3136.e	56.e	$2$	$8$	$8$	$25.041$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}^{2}q^{3}+\zeta_{16}^{7}q^{5}+(1-\zeta_{16}^{4}+\cdots)q^{9}+\cdots\)
3136.2.e.d	$3136$	$2$	3136.e	56.e	$2$	$12$	$12$	$25.041$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
3136.2.e.e	$3136$	$2$	3136.e	56.e	$2$	$12$	$12$	$25.041$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{3}+(1-\beta _{1})q^{5}+(-1-\beta _{2}+\cdots)q^{9}+\cdots\)
3136.2.e.f	$3136$	$2$	3136.e	56.e	$2$	$32$	$32$	$25.041$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3136, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1568, [\chi])\)\(^{\oplus 2}\)