Space of modular forms of level 14, weight 13, and Character 14.b

• Label: 14.13.b
• Level: $14$
• Weight: $13$
• Character orbit: 14.b
• Rep. character: $\chi_{14}(13,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $26$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(26\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(14, [\chi])\).

	Total	New	Old
Modular forms	26	8	18
Cusp forms	22	8	14
Eisenstein series	4	0	4

Trace form

\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9} + O(q^{10}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(14, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
14.13.b.a	$14$	$13$	14.b	7.b	$2$	$8$	$8$	$12.796$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(195160\)	$2^{26}\cdot 3^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+2^{11}q^{4}+(-11\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{13}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{13}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{13}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)