LMFDB - Space of modular forms of level 4400, weight 2, and Character 4400.b

Defining parameters

Level:	$ N $	$=$	$ 4400 = 2^{4} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4400.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 5 $
Character field:			$\Q$
Newform subspaces:			$ 29 $
Sturm bound:			$1440$
Trace bound:			$19$
Distinguishing $T_p$:			$3$, $7$, $13$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(4400, [\chi])$.

	Total	New	Old
Modular forms	756	90	666
Cusp forms	684	90	594
Eisenstein series	72	0	72

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(4400, [\chi])$ 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
4400.2.b.a	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+3iq^{3}-iq^{7}-6q^{9}+q^{11}+6iq^{13}+\cdots$
4400.2.b.b	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+3iq^{3}-2iq^{7}-6q^{9}+q^{11}+6iq^{17}+\cdots$
4400.2.b.c	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{3}-q^{9}-q^{11}-2iq^{17}-4q^{19}+\cdots$
4400.2.b.d	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+2iq^{3}-q^{9}-q^{11}-3iq^{13}-4iq^{17}+\cdots$
4400.2.b.e	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+2iq^{3}-4iq^{7}-q^{9}+q^{11}+5iq^{13}+\cdots$
4400.2.b.f	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{3}-2iq^{7}-q^{9}+q^{11}-2iq^{13}+\cdots$
4400.2.b.g	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{3}-5iq^{7}+2q^{9}-q^{11}-2iq^{13}+\cdots$
4400.2.b.h	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{3}-2iq^{7}+2q^{9}-q^{11}+4iq^{13}+\cdots$
4400.2.b.i	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{3}+3iq^{7}+2q^{9}-q^{11}-6iq^{13}+\cdots$
4400.2.b.j	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{3}+iq^{7}+2q^{9}+q^{11}-2iq^{13}+\cdots$
4400.2.b.k	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+iq^{3}-2iq^{7}+2q^{9}+q^{11}+4iq^{13}+\cdots$
4400.2.b.l	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q-iq^{7}+3q^{9}-q^{11}-2iq^{13}+2iq^{17}+\cdots$
4400.2.b.m	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q-iq^{7}+3q^{9}+q^{11}-8q^{19}+4iq^{23}+\cdots$
4400.2.b.n	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q+3q^{9}+q^{11}-iq^{13}+3iq^{17}-4q^{19}+\cdots$
4400.2.b.o	$2$	$35.134$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$0$	$0$	$q-2iq^{7}+3q^{9}+q^{11}-3iq^{13}-3iq^{17}+\cdots$
4400.2.b.p	$4$	$35.134$	$\Q(i, \sqrt{33})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+\beta _{1}q^{7}+(-6+\beta _{3})q^{9}+q^{11}+\cdots$
4400.2.b.q	$4$	$35.134$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$	$q+\zeta_{8}^{2}q^{3}-\zeta_{8}q^{7}-5q^{9}-q^{11}+(-2\zeta_{8}+\cdots)q^{13}+\cdots$
4400.2.b.r	$4$	$35.134$	$\Q(i, \sqrt{13})$	None	$0$	$0$	$0$	$0$	$q+(\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-4+\cdots)q^{9}+\cdots$
4400.2.b.s	$4$	$35.134$	$\Q(i, \sqrt{21})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-3+\beta _{3})q^{9}+\cdots$
4400.2.b.t	$4$	$35.134$	$\Q(i, \sqrt{17})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{3})q^{9}-q^{11}+\cdots$
4400.2.b.u	$4$	$35.134$	$\Q(i, \sqrt{17})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots$
4400.2.b.v	$4$	$35.134$	$\Q(i, \sqrt{17})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots$
4400.2.b.w	$4$	$35.134$	$\Q(i, \sqrt{17})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots$
4400.2.b.x	$4$	$35.134$	$\Q(i, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$q+(\beta _{1}-\beta _{3})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots$
4400.2.b.y	$4$	$35.134$	$\Q(i, \sqrt{13})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots$
4400.2.b.z	$4$	$35.134$	$\Q(i, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots$
4400.2.b.ba	$4$	$35.134$	$\Q(i, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots$
4400.2.b.bb	$6$	$35.134$	6.0.96668224.1	None	$0$	$0$	$0$	$0$	$q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{4})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots$
4400.2.b.bc	$6$	$35.134$	6.0.44836416.1	None	$0$	$0$	$0$	$0$	$q+(\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(4400, [\chi])$ into lower level spaces

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Level:	\( N \)	\(=\)	\( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4400.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(1440\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\), \(17\)

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
4400.2.b.a	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+3iq^{3}-iq^{7}-6q^{9}+q^{11}+6iq^{13}+\cdots\)
4400.2.b.b	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+3iq^{3}-2iq^{7}-6q^{9}+q^{11}+6iq^{17}+\cdots\)
4400.2.b.c	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{3}-q^{9}-q^{11}-2iq^{17}-4q^{19}+\cdots\)
4400.2.b.d	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+2iq^{3}-q^{9}-q^{11}-3iq^{13}-4iq^{17}+\cdots\)
4400.2.b.e	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+2iq^{3}-4iq^{7}-q^{9}+q^{11}+5iq^{13}+\cdots\)
4400.2.b.f	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{3}-2iq^{7}-q^{9}+q^{11}-2iq^{13}+\cdots\)
4400.2.b.g	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{3}-5iq^{7}+2q^{9}-q^{11}-2iq^{13}+\cdots\)
4400.2.b.h	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{3}-2iq^{7}+2q^{9}-q^{11}+4iq^{13}+\cdots\)
4400.2.b.i	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{3}+3iq^{7}+2q^{9}-q^{11}-6iq^{13}+\cdots\)
4400.2.b.j	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{3}+iq^{7}+2q^{9}+q^{11}-2iq^{13}+\cdots\)
4400.2.b.k	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+iq^{3}-2iq^{7}+2q^{9}+q^{11}+4iq^{13}+\cdots\)
4400.2.b.l	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{7}+3q^{9}-q^{11}-2iq^{13}+2iq^{17}+\cdots\)
4400.2.b.m	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-iq^{7}+3q^{9}+q^{11}-8q^{19}+4iq^{23}+\cdots\)
4400.2.b.n	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+3q^{9}+q^{11}-iq^{13}+3iq^{17}-4q^{19}+\cdots\)
4400.2.b.o	\(2\)	\(35.134\)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q-2iq^{7}+3q^{9}+q^{11}-3iq^{13}-3iq^{17}+\cdots\)
4400.2.b.p	\(4\)	\(35.134\)	\(\Q(i, \sqrt{33})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+\beta _{1}q^{7}+(-6+\beta _{3})q^{9}+q^{11}+\cdots\)
4400.2.b.q	\(4\)	\(35.134\)	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\zeta_{8}^{2}q^{3}-\zeta_{8}q^{7}-5q^{9}-q^{11}+(-2\zeta_{8}+\cdots)q^{13}+\cdots\)
4400.2.b.r	\(4\)	\(35.134\)	\(\Q(i, \sqrt{13})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(\beta _{1}-\beta _{2})q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-4+\cdots)q^{9}+\cdots\)
4400.2.b.s	\(4\)	\(35.134\)	\(\Q(i, \sqrt{21})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
4400.2.b.t	\(4\)	\(35.134\)	\(\Q(i, \sqrt{17})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}-\beta _{1}q^{7}+(-2+\beta _{3})q^{9}-q^{11}+\cdots\)
4400.2.b.u	\(4\)	\(35.134\)	\(\Q(i, \sqrt{17})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4400.2.b.v	\(4\)	\(35.134\)	\(\Q(i, \sqrt{17})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4400.2.b.w	\(4\)	\(35.134\)	\(\Q(i, \sqrt{17})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4400.2.b.x	\(4\)	\(35.134\)	\(\Q(i, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(\beta _{1}-\beta _{3})q^{3}+(3\beta _{1}+2\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
4400.2.b.y	\(4\)	\(35.134\)	\(\Q(i, \sqrt{13})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+(\beta _{1}+3\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots\)
4400.2.b.z	\(4\)	\(35.134\)	\(\Q(i, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
4400.2.b.ba	\(4\)	\(35.134\)	\(\Q(i, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
4400.2.b.bb	\(6\)	\(35.134\)	6.0.96668224.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+\beta _{1}q^{3}+(-\beta _{2}-\beta _{4})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)
4400.2.b.bc	\(6\)	\(35.134\)	6.0.44836416.1	None	\(0\)	\(0\)	\(0\)	\(0\)	\(q+(\beta _{1}+\beta _{3})q^{3}+(-\beta _{3}-\beta _{5})q^{7}+(-2+\cdots)q^{9}+\cdots\)

Introduction

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(4400, [\chi])\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(4400, [\chi])\) 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	4400.2.b

Level	$4400$
Weight	$2$
Character orbit	4400.b
Rep. character	$\chi_{4400}(4049,\cdot)$
Character field	$\Q$
Dimension	$90$
Newform subspaces	$29$
Sturm bound	$1440$
Trace bound	$19$