LMFDB - Space of modular forms of level 3850, weight 2, and Character 3850.c

Defining parameters

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.c (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 5 $
Character field:			$\Q$
Newform subspaces:			$ 29 $
Sturm bound:			$1440$
Trace bound:			$29$
Distinguishing $T_p$:			$3$, $13$, $17$, $19$, $37$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3850, [\chi])$.

	Total	New	Old
Modular forms	744	92	652
Cusp forms	696	92	604
Eisenstein series	48	0	48

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(3850, [\chi])$ 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
3850.2.c.a	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots$
3850.2.c.b	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots$
3850.2.c.c	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{7}+\cdots$
3850.2.c.d	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots$
3850.2.c.e	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots$
3850.2.c.f	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots$
3850.2.c.g	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots$
3850.2.c.h	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}-q^{4}+iq^{7}-iq^{8}+3q^{9}+\cdots$
3850.2.c.i	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q-iq^{2}-q^{4}-iq^{7}+iq^{8}+3q^{9}+\cdots$
3850.2.c.j	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q-iq^{2}-q^{4}-iq^{7}+iq^{8}+3q^{9}+\cdots$
3850.2.c.k	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q-iq^{2}-q^{4}+iq^{7}+iq^{8}+3q^{9}+\cdots$
3850.2.c.l	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots$
3850.2.c.m	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots$
3850.2.c.n	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots$
3850.2.c.o	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{7}+\cdots$
3850.2.c.p	$2$	$30.742$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots$
3850.2.c.q	$4$	$30.742$	$\Q(i, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots$
3850.2.c.r	$4$	$30.742$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$0$	$q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots$
3850.2.c.s	$4$	$30.742$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$0$	$q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots$
3850.2.c.t	$4$	$30.742$	$\Q(i, \sqrt{10})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots$
3850.2.c.u	$4$	$30.742$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$	$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots$
3850.2.c.v	$4$	$30.742$	$\Q(i, \sqrt{7})$	None	$0$	$0$	$0$	$0$	$q-\beta _{1}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots$
3850.2.c.w	$4$	$30.742$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$	$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots$
3850.2.c.x	$4$	$30.742$	$\Q(\zeta_{12})$	None	$0$	$0$	$0$	$0$	$q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots$
3850.2.c.y	$4$	$30.742$	$\Q(i, \sqrt{33})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{2}-2\beta _{1}q^{3}-q^{4}+2q^{6}+\beta _{1}q^{7}+\cdots$
3850.2.c.z	$6$	$30.742$	6.0.3182656.1	None	$0$	$0$	$0$	$0$	$q-\beta _{4}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{4}q^{7}+\cdots$
3850.2.c.ba	$6$	$30.742$	6.0.399424.1	None	$0$	$0$	$0$	$0$	$q-\beta _{2}q^{2}+(\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots$
3850.2.c.bb	$6$	$30.742$	6.0.399424.1	None	$0$	$0$	$0$	$0$	$q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\cdots)q^{6}+\cdots$
3850.2.c.bc	$6$	$30.742$	6.0.3534400.1	None	$0$	$0$	$0$	$0$	$q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(3850, [\chi])$ into lower level spaces

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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(1440\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(3\), \(13\), \(17\), \(19\), \(37\)

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
3850.2.c.a	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots\)
3850.2.c.b	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots\)
3850.2.c.c	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-iq^{7}+\cdots\)
3850.2.c.d	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots\)
3850.2.c.e	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+iq^{7}+\cdots\)
3850.2.c.f	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
3850.2.c.g	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
3850.2.c.h	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+3q^{9}+\cdots\)
3850.2.c.i	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+3q^{9}+\cdots\)
3850.2.c.j	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+3q^{9}+\cdots\)
3850.2.c.k	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+3q^{9}+\cdots\)
3850.2.c.l	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots\)
3850.2.c.m	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+3q^{9}+\cdots\)
3850.2.c.n	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{2}+iq^{3}-q^{4}+q^{6}-iq^{7}+iq^{8}+\cdots\)
3850.2.c.o	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+iq^{7}+\cdots\)
3850.2.c.p	\(2\)	\(30.742\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-iq^{7}+\cdots\)
3850.2.c.q	\(4\)	\(30.742\)	\(\Q(i, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots\)
3850.2.c.r	\(4\)	\(30.742\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
3850.2.c.s	\(4\)	\(30.742\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
3850.2.c.t	\(4\)	\(30.742\)	\(\Q(i, \sqrt{10})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{3}q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.u	\(4\)	\(30.742\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots\)
3850.2.c.v	\(4\)	\(30.742\)	\(\Q(i, \sqrt{7})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.w	\(4\)	\(30.742\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots\)
3850.2.c.x	\(4\)	\(30.742\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
3850.2.c.y	\(4\)	\(30.742\)	\(\Q(i, \sqrt{33})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{2}-2\beta _{1}q^{3}-q^{4}+2q^{6}+\beta _{1}q^{7}+\cdots\)
3850.2.c.z	\(6\)	\(30.742\)	6.0.3182656.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\beta _{4}q^{2}+\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{4}q^{7}+\cdots\)
3850.2.c.ba	\(6\)	\(30.742\)	6.0.399424.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
3850.2.c.bb	\(6\)	\(30.742\)	6.0.399424.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{2}q^{2}+(-\beta _{2}+\beta _{5})q^{3}-q^{4}+(1+\cdots)q^{6}+\cdots\)
3850.2.c.bc	\(6\)	\(30.742\)	6.0.3534400.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\beta _{4}q^{2}+(\beta _{4}+\beta _{5})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(3850, [\chi])\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(3850, [\chi])\) 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	3850.2.c

Level	$3850$
Weight	$2$
Character orbit	3850.c
Rep. character	$\chi_{3850}(1849,\cdot)$
Character field	$\Q$
Dimension	$92$
Newform subspaces	$29$
Sturm bound	$1440$
Trace bound	$29$