LMFDB - Space of modular forms of level 3200, weight 2, and Character 3200.d

Defining parameters

Level:	$ N $	$=$	$ 3200 = 2^{7} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3200.d (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 8 $
Character field:			$\Q$
Newform subspaces:			$ 23 $
Sturm bound:			$960$
Trace bound:			$33$
Distinguishing $T_p$:			$3$, $7$, $11$, $13$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3200, [\chi])$.

	Total	New	Old
Modular forms	528	76	452
Cusp forms	432	76	356
Eisenstein series	96	0	96

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(3200, [\chi])$ 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
3200.2.d.a	$2$	$25.552$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$-8$	$q+iq^{3}-4q^{7}+2q^{9}-3iq^{11}-q^{17}+\cdots$
3200.2.d.b	$2$	$25.552$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$-8$	$q+iq^{3}-4q^{7}+2q^{9}+3iq^{11}+q^{17}+\cdots$
3200.2.d.c	$2$	$25.552$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $	$0$	$0$	$0$	$0$	$q+\beta q^{3}-5q^{9}-\beta q^{11}-6q^{17}+3\beta q^{19}+\cdots$
3200.2.d.d	$2$	$25.552$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	$0$	$0$	$0$	$0$	$q+3q^{9}-3iq^{13}-8q^{17}-2iq^{29}+\cdots$
3200.2.d.e	$2$	$25.552$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	$0$	$0$	$0$	$0$	$q+3q^{9}-iq^{13}+2q^{17}+iq^{29}-3iq^{37}+\cdots$
3200.2.d.f	$2$	$25.552$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	$0$	$0$	$0$	$0$	$q+3q^{9}+3iq^{13}+8q^{17}-2iq^{29}+\cdots$
3200.2.d.g	$2$	$25.552$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$8$	$q+iq^{3}+4q^{7}+2q^{9}-3iq^{11}-q^{17}+\cdots$
3200.2.d.h	$2$	$25.552$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$8$	$q+iq^{3}+4q^{7}+2q^{9}+3iq^{11}+q^{17}+\cdots$
3200.2.d.i	$4$	$25.552$	$\Q(\sqrt{2}, \sqrt{-5})$	$\Q(\sqrt{-5}) $	$0$	$0$	$0$	$0$	$q+\beta _{2}q^{3}-3\beta _{1}q^{7}-7q^{9}+3\beta _{3}q^{21}+\cdots$
3200.2.d.j	$4$	$25.552$	$\Q(i, \sqrt{10})$	None	$0$	$0$	$0$	$0$	$q+\beta _{2}q^{3}-\beta _{3}q^{7}-7q^{9}+3\beta _{1}q^{13}+\cdots$
3200.2.d.k	$4$	$25.552$	$\Q(i, \sqrt{6})$	None	$0$	$0$	$0$	$0$	$q+\beta _{2}q^{3}-\beta _{3}q^{7}-3q^{9}-2\beta _{2}q^{11}+\cdots$
3200.2.d.l	$4$	$25.552$	$\Q(i, \sqrt{6})$	None	$0$	$0$	$0$	$0$	$q+\beta _{2}q^{3}+\beta _{3}q^{7}-3q^{9}+2\beta _{2}q^{11}+\cdots$
3200.2.d.m	$4$	$25.552$	$\Q(\sqrt{2}, \sqrt{-5})$	None	$0$	$0$	$0$	$0$	$q+\beta _{3}q^{3}+\beta _{1}q^{7}-2q^{9}+\beta _{3}q^{11}+\cdots$
3200.2.d.n	$4$	$25.552$	$\Q(\sqrt{-2}, \sqrt{-3})$	$\Q(\sqrt{-2}) $	$0$	$0$	$0$	$0$	$q+\beta _{2}q^{3}+(-2+\beta _{3})q^{9}+(\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots$
3200.2.d.o	$4$	$25.552$	$\Q(i, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$q-\beta _{1}q^{3}-2q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots$
3200.2.d.p	$4$	$25.552$	$\Q(i, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}-2q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots$
3200.2.d.q	$4$	$25.552$	$\Q(\sqrt{-2}, \sqrt{-3})$	$\Q(\sqrt{-2}) $	$0$	$0$	$0$	$0$	$q+\beta _{2}q^{3}+(-2+\beta _{3})q^{9}+(-\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots$
3200.2.d.r	$4$	$25.552$	$\Q(\sqrt{2}, \sqrt{-5})$	None	$0$	$0$	$0$	$0$	$q+\beta _{3}q^{3}-\beta _{1}q^{7}-2q^{9}-\beta _{3}q^{11}+\cdots$
3200.2.d.s	$4$	$25.552$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$	$q+\zeta_{8}^{2}q^{3}+3\zeta_{8}^{3}q^{7}+q^{9}+4\zeta_{8}^{2}q^{11}+\cdots$
3200.2.d.t	$4$	$25.552$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$	$q+\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{7}+q^{9}-2\zeta_{8}^{2}q^{11}+\cdots$
3200.2.d.u	$4$	$25.552$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-5}) $	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+\beta _{2}q^{7}+q^{9}+\beta _{3}q^{21}-3\beta _{2}q^{23}+\cdots$
3200.2.d.v	$4$	$25.552$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$	$q+\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{7}+q^{9}+2\zeta_{8}^{2}q^{11}+\cdots$
3200.2.d.w	$4$	$25.552$	$\Q(\sqrt{2}, \sqrt{-5})$	$\Q(\sqrt{-10}) $	$0$	$0$	$0$	$0$	$q-\beta _{1}q^{7}+3q^{9}-\beta _{2}q^{11}+\beta _{3}q^{13}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(3200, [\chi])$ into lower level spaces

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

Level:	\( N \)	\(=\)	\( 3200 = 2^{7} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3200.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 23 \)
Sturm bound:			\(960\)
Trace bound:			\(33\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\), \(17\)

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
3200.2.d.a	\(2\)	\(25.552\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(-8\)	\(q+iq^{3}-4q^{7}+2q^{9}-3iq^{11}-q^{17}+\cdots\)
3200.2.d.b	\(2\)	\(25.552\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(-8\)	\(q+iq^{3}-4q^{7}+2q^{9}+3iq^{11}+q^{17}+\cdots\)
3200.2.d.c	\(2\)	\(25.552\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta q^{3}-5q^{9}-\beta q^{11}-6q^{17}+3\beta q^{19}+\cdots\)
3200.2.d.d	\(2\)	\(25.552\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+3q^{9}-3iq^{13}-8q^{17}-2iq^{29}+\cdots\)
3200.2.d.e	\(2\)	\(25.552\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+3q^{9}-iq^{13}+2q^{17}+iq^{29}-3iq^{37}+\cdots\)
3200.2.d.f	\(2\)	\(25.552\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+3q^{9}+3iq^{13}+8q^{17}-2iq^{29}+\cdots\)
3200.2.d.g	\(2\)	\(25.552\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(8\)	\(q+iq^{3}+4q^{7}+2q^{9}-3iq^{11}-q^{17}+\cdots\)
3200.2.d.h	\(2\)	\(25.552\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(8\)	\(q+iq^{3}+4q^{7}+2q^{9}+3iq^{11}+q^{17}+\cdots\)
3200.2.d.i	\(4\)	\(25.552\)	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{2}q^{3}-3\beta _{1}q^{7}-7q^{9}+3\beta _{3}q^{21}+\cdots\)
3200.2.d.j	\(4\)	\(25.552\)	\(\Q(i, \sqrt{10})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{2}q^{3}-\beta _{3}q^{7}-7q^{9}+3\beta _{1}q^{13}+\cdots\)
3200.2.d.k	\(4\)	\(25.552\)	\(\Q(i, \sqrt{6})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{2}q^{3}-\beta _{3}q^{7}-3q^{9}-2\beta _{2}q^{11}+\cdots\)
3200.2.d.l	\(4\)	\(25.552\)	\(\Q(i, \sqrt{6})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{2}q^{3}+\beta _{3}q^{7}-3q^{9}+2\beta _{2}q^{11}+\cdots\)
3200.2.d.m	\(4\)	\(25.552\)	\(\Q(\sqrt{2}, \sqrt{-5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{3}q^{3}+\beta _{1}q^{7}-2q^{9}+\beta _{3}q^{11}+\cdots\)
3200.2.d.n	\(4\)	\(25.552\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{9}+(\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots\)
3200.2.d.o	\(4\)	\(25.552\)	\(\Q(i, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\beta _{1}q^{3}-2q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)
3200.2.d.p	\(4\)	\(25.552\)	\(\Q(i, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}-2q^{9}+\beta _{1}q^{11}-\beta _{2}q^{13}+\cdots\)
3200.2.d.q	\(4\)	\(25.552\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{9}+(-\beta _{1}-2\beta _{2}+\cdots)q^{11}+\cdots\)
3200.2.d.r	\(4\)	\(25.552\)	\(\Q(\sqrt{2}, \sqrt{-5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{3}q^{3}-\beta _{1}q^{7}-2q^{9}-\beta _{3}q^{11}+\cdots\)
3200.2.d.s	\(4\)	\(25.552\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{8}^{2}q^{3}+3\zeta_{8}^{3}q^{7}+q^{9}+4\zeta_{8}^{2}q^{11}+\cdots\)
3200.2.d.t	\(4\)	\(25.552\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{7}+q^{9}-2\zeta_{8}^{2}q^{11}+\cdots\)
3200.2.d.u	\(4\)	\(25.552\)	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+\beta _{2}q^{7}+q^{9}+\beta _{3}q^{21}-3\beta _{2}q^{23}+\cdots\)
3200.2.d.v	\(4\)	\(25.552\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{8}^{2}q^{3}-\zeta_{8}^{3}q^{7}+q^{9}+2\zeta_{8}^{2}q^{11}+\cdots\)
3200.2.d.w	\(4\)	\(25.552\)	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)	\(0\)	\(0\)	\(0\)	\(0\)	\(q-\beta _{1}q^{7}+3q^{9}-\beta _{2}q^{11}+\beta _{3}q^{13}+\cdots\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(3200, [\chi])\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(3200, [\chi])\) 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	3200.2.d

Level	$3200$
Weight	$2$
Character orbit	3200.d
Rep. character	$\chi_{3200}(1601,\cdot)$
Character field	$\Q$
Dimension	$76$
Newform subspaces	$23$
Sturm bound	$960$
Trace bound	$33$