LMFDB - Space of Modular Forms of Level 31, Weight 2, and Character 31.d

Defining parameters

Level:	$ N $	=	$ 31 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	31.d (of order $5$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	=	$ 31 $
Character field:			$\Q(\zeta_{5})$
Newforms:			$ 1 $
Sturm bound:			$5$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(31, [\chi])$.

	Total	New
Modular forms	12	12
Cusp forms	4	4
Eisenstein series	8	8

Trace form

$4q $ $\mathstrut -\mathstrut 3q^{2} $ $\mathstrut +\mathstrut q^{3} $ $\mathstrut +\mathstrut 3q^{4} $ $\mathstrut -\mathstrut 6q^{5} $ $\mathstrut -\mathstrut 2q^{6} $ $\mathstrut -\mathstrut 3q^{7} $ $\mathstrut -\mathstrut 5q^{8} $ $\mathstrut +\mathstrut 2q^{9} $ $\mathstrut +\mathstrut 2q^{10} $ $\mathstrut -\mathstrut 2q^{11} $ $\mathstrut +\mathstrut 2q^{12} $ $\mathstrut +\mathstrut 6q^{13} $ $\mathstrut +\mathstrut 6q^{14} $ $\mathstrut +\mathstrut q^{15} $ $\mathstrut +\mathstrut 9q^{16} $ $\mathstrut -\mathstrut 3q^{17} $ $\mathstrut +\mathstrut 6q^{18} $ $\mathstrut -\mathstrut 5q^{19} $ $\mathstrut -\mathstrut 7q^{20} $ $\mathstrut +\mathstrut 3q^{21} $ $\mathstrut -\mathstrut 6q^{22} $ $\mathstrut +\mathstrut 11q^{23} $ $\mathstrut +\mathstrut 5q^{24} $ $\mathstrut -\mathstrut 6q^{25} $ $\mathstrut -\mathstrut 12q^{26} $ $\mathstrut -\mathstrut 5q^{27} $ $\mathstrut -\mathstrut 6q^{28} $ $\mathstrut +\mathstrut 5q^{29} $ $\mathstrut -\mathstrut 2q^{30} $ $\mathstrut -\mathstrut 11q^{31} $ $\mathstrut -\mathstrut 18q^{32} $ $\mathstrut -\mathstrut 8q^{33} $ $\mathstrut +\mathstrut 11q^{34} $ $\mathstrut +\mathstrut 12q^{35} $ $\mathstrut +\mathstrut 4q^{36} $ $\mathstrut -\mathstrut 8q^{37} $ $\mathstrut +\mathstrut 10q^{38} $ $\mathstrut +\mathstrut 9q^{39} $ $\mathstrut +\mathstrut 10q^{40} $ $\mathstrut +\mathstrut 8q^{41} $ $\mathstrut -\mathstrut 6q^{42} $ $\mathstrut +\mathstrut q^{43} $ $\mathstrut +\mathstrut 6q^{44} $ $\mathstrut -\mathstrut 8q^{45} $ $\mathstrut -\mathstrut 7q^{46} $ $\mathstrut +\mathstrut 7q^{47} $ $\mathstrut +\mathstrut 6q^{48} $ $\mathstrut -\mathstrut 2q^{49} $ $\mathstrut +\mathstrut 12q^{50} $ $\mathstrut +\mathstrut 3q^{51} $ $\mathstrut -\mathstrut 3q^{52} $ $\mathstrut +\mathstrut 21q^{53} $ $\mathstrut +\mathstrut 10q^{54} $ $\mathstrut -\mathstrut 2q^{55} $ $\mathstrut -\mathstrut 20q^{57} $ $\mathstrut -\mathstrut 15q^{58} $ $\mathstrut +\mathstrut 5q^{59} $ $\mathstrut -\mathstrut 3q^{60} $ $\mathstrut +\mathstrut 8q^{61} $ $\mathstrut -\mathstrut 8q^{62} $ $\mathstrut -\mathstrut 24q^{63} $ $\mathstrut -\mathstrut 7q^{64} $ $\mathstrut -\mathstrut 9q^{65} $ $\mathstrut +\mathstrut 6q^{66} $ $\mathstrut -\mathstrut 8q^{67} $ $\mathstrut -\mathstrut 6q^{68} $ $\mathstrut -\mathstrut 11q^{69} $ $\mathstrut -\mathstrut 9q^{70} $ $\mathstrut -\mathstrut 7q^{71} $ $\mathstrut -\mathstrut 10q^{72} $ $\mathstrut +\mathstrut 21q^{73} $ $\mathstrut +\mathstrut 11q^{74} $ $\mathstrut -\mathstrut 9q^{75} $ $\mathstrut +\mathstrut 15q^{76} $ $\mathstrut +\mathstrut 24q^{77} $ $\mathstrut -\mathstrut 3q^{78} $ $\mathstrut -\mathstrut 6q^{80} $ $\mathstrut -\mathstrut q^{81} $ $\mathstrut +\mathstrut 4q^{82} $ $\mathstrut -\mathstrut 14q^{83} $ $\mathstrut -\mathstrut 9q^{84} $ $\mathstrut +\mathstrut 2q^{85} $ $\mathstrut -\mathstrut 7q^{86} $ $\mathstrut +\mathstrut 30q^{87} $ $\mathstrut +\mathstrut 20q^{88} $ $\mathstrut +\mathstrut 5q^{89} $ $\mathstrut -\mathstrut 4q^{90} $ $\mathstrut +\mathstrut 18q^{91} $ $\mathstrut +\mathstrut 22q^{92} $ $\mathstrut -\mathstrut 4q^{93} $ $\mathstrut -\mathstrut 14q^{94} $ $\mathstrut -\mathstrut 5q^{95} $ $\mathstrut -\mathstrut 2q^{96} $ $\mathstrut -\mathstrut 3q^{97} $ $\mathstrut +\mathstrut 4q^{98} $ $\mathstrut +\mathstrut 24q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(31, [\chi])$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
31.2.d.a	$4$	$0.248$	$\Q(\zeta_{10})$	None	$-3$	$1$	$-6$	$-3$	$q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 31 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	31.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 31 \)
Character field:			\(\Q(\zeta_{5})\)
Newforms:			\( 1 \)
Sturm bound:			\(5\)
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
31.2.d.a	\(4\)	\(0.248\)	\(\Q(\zeta_{10})\)	None	\(-3\)	\(1\)	\(-6\)	\(-3\)	\(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(31, [\chi])\) into irreducible Hecke orbits

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	31.2.d

Level	31
Weight	2
Character orbit	d
Rep. character	\(\chi_{31}(2,\cdot)\)
Character field	\(\Q(\zeta_{5})\)
Dimension	4
Newforms	1
Sturm bound	5
Trace bound	0