LMFDB - Space of modular forms of level 961, weight 2, and Character 961.d

Defining parameters

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 31 $
Character field:			$\Q(\zeta_{5})$
Newform subspaces:			$ 19 $
Sturm bound:			$165$
Trace bound:			$4$
Distinguishing $T_p$:			$2$, $3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(961, [\chi])$.

	Total	New	Old
Modular forms	392	368	24
Cusp forms	264	256	8
Eisenstein series	128	112	16

Trace form

$ 256 q + 3 q^{2} - q^{3} - 53 q^{4} + 6 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 37 q^{9} + O(q^{10}) $

\( 256 q + 3 q^{2} - q^{3} - 53 q^{4} + 6 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 37 q^{9} - 5 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} - 9 q^{14} - q^{15} - 29 q^{16} + 3 q^{17} - 6 q^{18} + 5 q^{19} + 4 q^{20} - 3 q^{21} + 6 q^{22} - 11 q^{23} - 5 q^{24} + 26 q^{25} + 12 q^{26} + 5 q^{27} + 3 q^{28} - 5 q^{29} + 2 q^{30} - 78 q^{32} + 8 q^{33} - 11 q^{34} - 18 q^{35} - 44 q^{36} + 8 q^{37} - 13 q^{38} - 13 q^{39} - 16 q^{40} - 12 q^{41} + 6 q^{42} - q^{43} - 6 q^{44} + 4 q^{45} + 7 q^{46} - 13 q^{47} - 6 q^{48} + 27 q^{49} - 15 q^{50} - 7 q^{51} + 3 q^{52} - 21 q^{53} - 10 q^{54} + 2 q^{55} + 24 q^{56} + 20 q^{57} + 15 q^{58} - 9 q^{59} + 3 q^{60} - 8 q^{61} - 64 q^{63} + 44 q^{64} + 9 q^{65} + 46 q^{66} + 32 q^{67} + 6 q^{68} + 7 q^{69} - 6 q^{70} - q^{71} - 5 q^{72} - 21 q^{73} - 11 q^{74} + 9 q^{75} - 30 q^{76} - 24 q^{77} - 5 q^{78} - 3 q^{80} + 52 q^{81} - 19 q^{82} + 14 q^{83} + 9 q^{84} - 2 q^{85} + 7 q^{86} + 2 q^{87} - 20 q^{88} - 5 q^{89} - 11 q^{90} - 18 q^{91} - 22 q^{92} - 90 q^{94} - 5 q^{95} + 2 q^{96} - q^{97} + 40 q^{98} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(961, [\chi])$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	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	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
961.2.d.a	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	None			31.2.a.a	$2$	$0$	$-3$	$-6$	$4$	$7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}+(-2+2\zeta_{10}^{3})q^{3}+\cdots$
961.2.d.b	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	None			31.2.d.a	$2$	$0$	$-3$	$-1$	$-6$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
961.2.d.c	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	None			31.2.a.a	$2$	$0$	$-3$	$6$	$4$	$7$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1-\zeta_{10}^{2})q^{2}+(2-2\zeta_{10}^{3})q^{3}+\cdots$
961.2.d.d	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	None			31.2.a.a	$2$	$0$	$2$	$-4$	$4$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-2\zeta_{10}+2\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
961.2.d.e	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	None			31.2.d.a	$2$	$0$	$2$	$-1$	$-6$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2})q^{2}+(-1+\zeta_{10}+\cdots)q^{3}+\cdots$
961.2.d.f	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	None			31.2.d.a	$2$	$0$	$2$	$1$	$-6$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
961.2.d.g	$961$	$2$	961.d	31.d	$5$	$4$	$1$	$7.674$	$\Q(\zeta_{10})$	None			31.2.a.a	$2$	$0$	$2$	$4$	$4$	$-3$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2})q^{2}+(2\zeta_{10}-2\zeta_{10}^{2}+\cdots)q^{3}+\cdots$
961.2.d.h	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	None		✓	961.2.a.h	$4$	$0$	$-8$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\beta _{2}+2\beta _{4}+\beta _{6})q^{2}+(\beta _{1}+\beta _{5}+\beta _{7})q^{3}+\cdots$
961.2.d.i	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	None			31.2.c.a	$4$	$0$	$2$	$-2$	$8$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}+\beta _{7})q^{2}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots$
961.2.d.j	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	None		✓	961.2.a.h	$4$	$0$	$2$	$0$	$0$	$2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+2\beta _{2}+\beta _{4})q^{2}+(\beta _{1}+\beta _{5})q^{3}+\cdots$
961.2.d.k	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	None		✓	961.2.a.b	$8$	$0$	$2$	$0$	$0$	$-8$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{6}q^{2}+(2\beta _{1}+2\beta _{3}+2\beta _{5}+2\beta _{7})q^{3}+\cdots$
961.2.d.l	$961$	$2$	961.d	31.d	$5$	$8$	$2$	$7.674$	8.0.64000000.2	None			31.2.c.a	$4$	$0$	$2$	$2$	$8$	$-2$	$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{2}+\beta _{7})q^{2}+(1+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$
961.2.d.m	$961$	$2$	961.d	31.d	$5$	$12$	$3$	$7.674$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$\Q(\sqrt{-31}) $		✓	961.2.a.g	$8$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{5}]$	$q+\beta _{9}q^{2}+(2\beta _{4}+\beta _{5})q^{4}+(\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
961.2.d.n	$961$	$2$	961.d	31.d	$5$	$16$	$4$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None			31.2.g.a	$2$	$0$	$-6$	$-9$	$6$	$11$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{3}+\beta _{9}+\beta _{10}+\beta _{11}+\beta _{15})q^{2}+\cdots$
961.2.d.o	$961$	$2$	961.d	31.d	$5$	$16$	$4$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None			31.2.g.a	$2$	$0$	$-6$	$9$	$6$	$11$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\beta _{3}+\beta _{9}+\beta _{10}+\beta _{11}+\beta _{15})q^{2}+\cdots$
961.2.d.p	$961$	$2$	961.d	31.d	$5$	$16$	$4$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None			31.2.g.a	$2$	$0$	$4$	$-6$	$6$	$-9$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{11}+\beta _{12}+\beta _{14})q^{2}+(-1+\cdots)q^{3}+\cdots$
961.2.d.q	$961$	$2$	961.d	31.d	$5$	$16$	$4$	$7.674$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None			31.2.g.a	$2$	$0$	$4$	$6$	$6$	$-9$	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{11}+\beta _{12}+\beta _{14})q^{2}+(1+\beta _{4}+\cdots)q^{3}+\cdots$
961.2.d.r	$961$	$2$	961.d	31.d	$5$	$48$	$12$	$7.674$		None		✓	961.2.a.k	$8$	$0$	$0$	$0$	$32$	$-8$		$\mathrm{SU}(2)[C_{5}]$
961.2.d.s	$961$	$2$	961.d	31.d	$5$	$64$	$16$	$7.674$		None		✓	961.2.a.l	$8$	$0$	$8$	$0$	$-64$	$16$		$\mathrm{SU}(2)[C_{5}]$

Decomposition of $S_{2}^{\mathrm{old}}(961, [\chi])$ into lower level spaces

$ S_{2}^{\mathrm{old}}(961, [\chi]) \simeq $ $S_{2}^{\mathrm{new}}(31, [\chi])$$^{\oplus 2}$

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Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(165\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(3\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(961, [\chi])\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(961, [\chi])\) into lower level spaces

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	961.2.d

Level	$961$
Weight	$2$
Character orbit	961.d
Rep. character	$\chi_{961}(374,\cdot)$
Character field	$\Q(\zeta_{5})$
Dimension	$256$
Newform subspaces	$19$
Sturm bound	$165$
Trace bound	$4$