Space of modular forms of level 1456, weight 2, and Character 1456.k

• Label: 1456.2.k
• Level: $1456$
• Weight: $2$
• Character orbit: 1456.k
• Rep. character: $\chi_{1456}(337,\cdot)$
• Character field: $\Q$
• Dimension: $42$
• Newform subspaces: $6$
• Sturm bound: $448$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1456.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(448\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1456, [\chi])\).

	Total	New	Old
Modular forms	236	42	194
Cusp forms	212	42	170
Eisenstein series	24	0	24

Trace form

\( 42 q + 42 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1456, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1456.2.k.a	$1456$	$2$	1456.k	13.b	$2$	$2$	$2$	$11.626$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+2iq^{5}-iq^{7}-2q^{9}-5iq^{11}+\cdots\)
1456.2.k.b	$1456$	$2$	1456.k	13.b	$2$	$6$	$6$	$11.626$	6.0.30647296.1	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots\)
1456.2.k.c	$1456$	$2$	1456.k	13.b	$2$	$6$	$6$	$11.626$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+\beta _{3}q^{7}+\cdots\)
1456.2.k.d	$1456$	$2$	1456.k	13.b	$2$	$8$	$8$	$11.626$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(\beta _{3}+\beta _{4})q^{5}+\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots\)
1456.2.k.e	$1456$	$2$	1456.k	13.b	$2$	$8$	$8$	$11.626$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{5})q^{5}+\beta _{5}q^{7}+\cdots\)
1456.2.k.f	$1456$	$2$	1456.k	13.b	$2$	$12$	$12$	$11.626$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{5}-\beta _{7})q^{5}-\beta _{4}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)