LMFDB - Space of modular forms of level 7, weight 10, and Character 7.c

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of $M_{10}(7, [\chi])$.

	Total	New
Modular forms	14	14
Cusp forms	10	10
Eisenstein series	4	4

Trace form

$ 10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9} + O(q^{10}) $

\( 10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9} + 4298 q^{10} + 42213 q^{11} + 135604 q^{12} - 319676 q^{13} - 39522 q^{14} + 151394 q^{15} + 322064 q^{16} + 324681 q^{17} - 1012868 q^{18} - 16121 q^{19} - 350616 q^{20} - 1557857 q^{21} - 62692 q^{22} + 2638863 q^{23} + 8449728 q^{24} - 1304092 q^{25} + 4179252 q^{26} - 18331558 q^{27} - 22156316 q^{28} + 15292500 q^{29} + 20557942 q^{30} + 19179237 q^{31} - 6263520 q^{32} + 1689359 q^{33} - 62909700 q^{34} - 43746759 q^{35} + 71476528 q^{36} + 39566985 q^{37} + 67365270 q^{38} - 44299486 q^{39} + 5721744 q^{40} - 53436852 q^{41} - 183129856 q^{42} + 101835992 q^{43} + 99704916 q^{44} + 85098230 q^{45} - 14489202 q^{46} + 32509659 q^{47} - 185141600 q^{48} - 49024598 q^{49} + 3328464 q^{50} + 44168403 q^{51} + 103893272 q^{52} - 25714707 q^{53} + 51200926 q^{54} - 144695222 q^{55} + 115352832 q^{56} - 121710346 q^{57} - 46645516 q^{58} + 46776513 q^{59} + 132391756 q^{60} - 113075039 q^{61} + 467465628 q^{62} + 318071530 q^{63} - 192008960 q^{64} - 338113566 q^{65} - 836682602 q^{66} - 126707879 q^{67} + 32262636 q^{68} + 1323616182 q^{69} + 697712470 q^{70} - 1188736032 q^{71} - 950557728 q^{72} - 859257651 q^{73} + 591757530 q^{74} - 169061732 q^{75} + 1101475592 q^{76} + 1911891891 q^{77} + 519432424 q^{78} - 527065417 q^{79} - 1257352656 q^{80} + 551662715 q^{81} - 1341703076 q^{82} - 144863208 q^{83} + 486452204 q^{84} - 1197360222 q^{85} - 678648216 q^{86} - 340781350 q^{87} + 903700608 q^{88} + 1661554797 q^{89} + 1967758744 q^{90} + 726641384 q^{91} - 1301840952 q^{92} - 423057489 q^{93} - 272580882 q^{94} - 1197123495 q^{95} - 1441922272 q^{96} + 869770188 q^{97} - 2404833858 q^{98} - 1900777180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{10}^{\mathrm{new}}(7, [\chi])$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	$q$-expansion
7.10.c.a	$10$	$3.605$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-18$	$161$	$1533$	$-1036$	$q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots$

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

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

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{10}^{\mathrm{new}}(7, [\chi])\) 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	7.10.c

Level	$7$
Weight	$10$
Character orbit	7.c
Rep. character	$\chi_{7}(2,\cdot)$
Character field	$\Q(\zeta_{3})$
Dimension	$10$
Newform subspaces	$1$
Sturm bound	$6$
Trace bound	$0$

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	$q$-expansion
7.10.c.a	$10$	$3.605$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-18\)	\(161\)	\(1533\)	\(-1036\)	\(q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots\)