LMFDB - Space of modular forms of level 847, weight 2, and Character 847.n

Defining parameters

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$ and degree $8$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 77 $
Character field:			$\Q(\zeta_{15})$
Newform subspaces:			$ 14 $
Sturm bound:			$176$
Trace bound:			$6$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(847, [\chi])$.

	Total	New	Old
Modular forms	800	640	160
Cusp forms	608	512	96
Eisenstein series	192	128	64

Trace form

$ 512 q + 5 q^{2} + 3 q^{3} + 61 q^{4} + q^{5} + 12 q^{6} + 7 q^{7} + 28 q^{8} + 45 q^{9} + O(q^{10}) $

\( 512 q + 5 q^{2} + 3 q^{3} + 61 q^{4} + q^{5} + 12 q^{6} + 7 q^{7} + 28 q^{8} + 45 q^{9} - 4 q^{10} - 24 q^{12} + 4 q^{13} - 8 q^{14} + 24 q^{15} + 35 q^{16} + 11 q^{17} - 18 q^{18} + 7 q^{19} + 48 q^{20} + 18 q^{21} - 42 q^{23} + 7 q^{24} + 9 q^{25} + 43 q^{26} + 6 q^{27} - 4 q^{28} - 24 q^{29} - 21 q^{30} + 9 q^{31} + 12 q^{32} - 296 q^{34} + 19 q^{35} - 42 q^{36} - 15 q^{37} - 13 q^{38} - 33 q^{39} - 5 q^{40} - 62 q^{41} + 32 q^{42} + 44 q^{43} - 24 q^{45} - 16 q^{46} - 21 q^{47} - 226 q^{48} + 15 q^{49} - 6 q^{50} + q^{51} + 3 q^{52} - 23 q^{53} - 44 q^{54} - 144 q^{56} - 20 q^{57} + 46 q^{58} - 7 q^{59} + 95 q^{60} - 18 q^{61} + 80 q^{62} - 22 q^{63} - 108 q^{64} + 10 q^{65} + 76 q^{67} + 21 q^{68} + 134 q^{69} - 37 q^{70} + 12 q^{71} + 48 q^{72} - 26 q^{73} + 55 q^{74} - 57 q^{75} + 144 q^{76} + 60 q^{78} - 30 q^{79} - 105 q^{80} + 55 q^{81} - 13 q^{82} + 28 q^{83} + 27 q^{84} + 98 q^{85} + 4 q^{86} - 66 q^{87} + 2 q^{89} + 18 q^{90} + 52 q^{91} + 74 q^{92} + 24 q^{93} - 45 q^{94} - 22 q^{95} + 55 q^{96} + 4 q^{97} - 120 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(847, [\chi])$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
847.2.n.a	$847$	$2$	847.n	77.m	$15$	$8$	$1$	$6.763$	$\Q(\zeta_{15})$	None		$4$	$0$	$-3$	$1$	$5$	$5$	$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-1-\zeta_{15}^{5}+\zeta_{15}^{7})q^{2}+(-1+\zeta_{15}+\cdots)q^{3}+\cdots$
847.2.n.b	$847$	$2$	847.n	77.m	$15$	$8$	$1$	$6.763$	$\Q(\zeta_{15})$	None		$4$	$0$	$2$	$1$	$-5$	$5$	$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(1-\zeta_{15}+\zeta_{15}^{5}-\zeta_{15}^{7})q^{2}+(-1+\cdots)q^{3}+\cdots$
847.2.n.c	$847$	$2$	847.n	77.m	$15$	$8$	$1$	$6.763$	$\Q(\zeta_{15})$	None		$4$	$0$	$3$	$1$	$5$	$-5$	$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(1+\zeta_{15}^{5}-\zeta_{15}^{7})q^{2}+(-1+\zeta_{15}+\cdots)q^{3}+\cdots$
847.2.n.d	$847$	$2$	847.n	77.m	$15$	$24$	$3$	$6.763$		None		$8$	$0$	$0$	$-1$	$-2$	$2$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.e	$847$	$2$	847.n	77.m	$15$	$24$	$3$	$6.763$		None		$8$	$0$	$0$	$-1$	$-2$	$-2$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.f	$847$	$2$	847.n	77.m	$15$	$24$	$3$	$6.763$		None		$8$	$0$	$0$	$3$	$6$	$0$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.g	$847$	$2$	847.n	77.m	$15$	$24$	$3$	$6.763$		None		$8$	$0$	$0$	$3$	$6$	$0$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.h	$847$	$2$	847.n	77.m	$15$	$40$	$5$	$6.763$		None		$4$	$0$	$-2$	$1$	$-6$	$-13$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.i	$847$	$2$	847.n	77.m	$15$	$40$	$5$	$6.763$		None		$4$	$0$	$2$	$1$	$-6$	$13$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.j	$847$	$2$	847.n	77.m	$15$	$40$	$5$	$6.763$		None		$4$	$0$	$3$	$-4$	$4$	$2$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.k	$847$	$2$	847.n	77.m	$15$	$48$	$6$	$6.763$		None		$16$	$0$	$0$	$-2$	$-4$	$0$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.l	$847$	$2$	847.n	77.m	$15$	$56$	$7$	$6.763$		None		$8$	$0$	$0$	$3$	$4$	$2$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.m	$847$	$2$	847.n	77.m	$15$	$56$	$7$	$6.763$		None		$8$	$0$	$0$	$3$	$4$	$-2$		$\mathrm{SU}(2)[C_{15}]$
847.2.n.n	$847$	$2$	847.n	77.m	$15$	$112$	$14$	$6.763$		None		$16$	$0$	$0$	$-6$	$-8$	$0$		$\mathrm{SU}(2)[C_{15}]$

Decomposition of $S_{2}^{\mathrm{old}}(847, [\chi])$ into lower level spaces

$ S_{2}^{\mathrm{old}}(847, [\chi]) \cong $ $S_{2}^{\mathrm{new}}(77, [\chi])$$^{\oplus 2}$

Overview	Random
Universe	Knowledge

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(176\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(847, [\chi])\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(847, [\chi])\) 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	847.2.n

Level	$847$
Weight	$2$
Character orbit	847.n
Rep. character	$\chi_{847}(9,\cdot)$
Character field	$\Q(\zeta_{15})$
Dimension	$512$
Newform subspaces	$14$
Sturm bound	$176$
Trace bound	$6$