LMFDB - Space of modular forms of level 21, weight 10, and Character 21.g

Defining parameters

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	21.g (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 21 $
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$ 1 $
Sturm bound:			$26$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{10}(21, [\chi])$.

	Total	New
Modular forms	52	52
Cusp forms	44	44
Eisenstein series	8	8

Trace form

$ 44 q - 3 q^{3} + 5118 q^{4} - 7504 q^{7} + 17745 q^{9} + 76890 q^{10} + 81456 q^{12} - 641226 q^{15} - 1273994 q^{16} + 625962 q^{18} - 1139244 q^{19} - 1975575 q^{21} + 5549324 q^{22} + 6080166 q^{24}+ \cdots + 1832627190 q^{99}+O(q^{100}) $

Decomposition of $S_{10}^{\mathrm{new}}(21, [\chi])$ 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
21.10.g.a	$21$	$10$	21.g	21.g	$6$	$44$	$22$	$10.816$		None		✓	✓	✓	21.10.g.a	$4$	$0$	$0$	$-3$	$0$	$-7504$		$\mathrm{SU}(2)[C_{6}]$

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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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(26\)
Trace bound:			\(0\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{10}^{\mathrm{new}}(21, [\chi])\) 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	21.10.g

Level	$21$
Weight	$10$
Character orbit	21.g
Rep. character	$\chi_{21}(5,\cdot)$
Character field	$\Q(\zeta_{6})$
Dimension	$44$
Newform subspaces	$1$
Sturm bound	$26$
Trace bound	$0$