Space of modular forms of level 35, weight 19, and Character 35.c

• Label: 35.19.c
• Level: $35$
• Weight: $19$
• Character orbit: 35.c
• Rep. character: $\chi_{35}(34,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $3$
• Sturm bound: $76$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(76\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(35, [\chi])\).

	Total	New	Old
Modular forms	74	74	0
Cusp forms	70	70	0
Eisenstein series	4	4	0

Trace form

\( 70 q - 8912900 q^{4} + 8183322258 q^{9} + O(q^{10}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(35, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.19.c.a	$35$	$19$	35.c	35.c	$2$	$1$	$1$	$71.885$	\(\Q\)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(-39286\)	\(1953125\)	\(-40353607\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-39286q^{3}+2^{18}q^{4}+5^{9}q^{5}-7^{9}q^{7}+\cdots\)
35.19.c.b	$35$	$19$	35.c	35.c	$2$	$1$	$1$	$71.885$	\(\Q\)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(39286\)	\(-1953125\)	\(40353607\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+39286q^{3}+2^{18}q^{4}-5^{9}q^{5}+7^{9}q^{7}+\cdots\)
35.19.c.c	$35$	$19$	35.c	35.c	$2$	$68$	$68$	$71.885$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$