LMFDB - Space of modular forms of level 35, weight 10, and Character 35.f

Defining parameters

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	35.f (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 35 $
Character field:			$\Q(i)$
Newform subspaces:			$ 1 $
Sturm bound:			$40$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{10}(35, [\chi])$.

	Total	New
Modular forms	76	76
Cusp forms	68	68
Eisenstein series	8	8

Trace form

$ 68 q - 4 q^{2} - 5946 q^{7} + 3472 q^{8} - 83032 q^{11} + 318860 q^{15} - 4744440 q^{16} + 357128 q^{18} + 999732 q^{21} - 4174596 q^{22} - 5819092 q^{23} - 38300 q^{25} + 17370560 q^{28} + 20856500 q^{30}+ \cdots + 8347561548 q^{98}+O(q^{100}) $

Decomposition of $S_{10}^{\mathrm{new}}(35, [\chi])$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
35.10.f.a	$35$	$10$	35.f	35.f	$4$	$68$	$34$	$18.026$		None		✓	✓	✓	35.10.f.a	$4$	$0$	$-4$	$0$	$0$	$-5946$		$\mathrm{SU}(2)[C_{4}]$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	35.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{10}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	35.10.f

Level	$35$
Weight	$10$
Character orbit	35.f
Rep. character	$\chi_{35}(13,\cdot)$
Character field	$\Q(\zeta_{4})$
Dimension	$68$
Newform subspaces	$1$
Sturm bound	$40$
Trace bound	$0$