Space of modular forms of level 35, weight 23, and Character 35.c

• Label: 35.23.c
• Level: $35$
• Weight: $23$
• Character orbit: 35.c
• Rep. character: $\chi_{35}(34,\cdot)$
• Character field: $\Q$
• Dimension: $86$
• Newform subspaces: $3$
• Sturm bound: $92$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 23 \)
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:			\(92\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(35, [\chi])\).

	Total	New	Old
Modular forms	90	90	0
Cusp forms	86	86	0
Eisenstein series	4	4	0

Trace form

\( 86 q - 176160772 q^{4} + 865839367488 q^{9} + O(q^{10}) \)

Decomposition of \(S_{23}^{\mathrm{new}}(35, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.23.c.a	$35$	$23$	35.c	35.c	$2$	$1$	$1$	$107.348$	\(\Q\)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(-341351\)	\(-48828125\)	\(1977326743\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-341351q^{3}+2^{22}q^{4}-5^{11}q^{5}+\cdots\)
35.23.c.b	$35$	$23$	35.c	35.c	$2$	$1$	$1$	$107.348$	\(\Q\)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(341351\)	\(48828125\)	\(-1977326743\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+341351q^{3}+2^{22}q^{4}+5^{11}q^{5}+\cdots\)
35.23.c.c	$35$	$23$	35.c	35.c	$2$	$84$	$84$	$107.348$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$