Space of modular forms of level 5328, weight 2, and Character 5328.h

• Label: 5328.2.h
• Level: $5328$
• Weight: $2$
• Character orbit: 5328.h
• Rep. character: $\chi_{5328}(2737,\cdot)$
• Character field: $\Q$
• Dimension: $94$
• Newform subspaces: $18$
• Sturm bound: $1824$
• Trace bound: $41$

Defining parameters

Level:	\( N \)	\(=\)	\( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5328.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1824\)
Trace bound:			\(41\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5328, [\chi])\).

	Total	New	Old
Modular forms	936	96	840
Cusp forms	888	94	794
Eisenstein series	48	2	46

Trace form

\( 94 q - 4 q^{7} - 94 q^{25} + 2 q^{37} - 4 q^{41} + 20 q^{47} + 86 q^{49} + 8 q^{53} - 8 q^{65} - 4 q^{67} + 4 q^{71} + 8 q^{77} + 12 q^{83} - 8 q^{85} - 8 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5328, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5328.2.h.a	$5328$	$2$	5328.h	37.b	$2$	$2$	$2$	$42.544$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					1332.2.e.b	$4$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-4 q^{7}+2\beta q^{13}+\beta q^{19}+5 q^{25}+\cdots\)
5328.2.h.b	$5328$	$2$	5328.h	37.b	$2$	$2$	$2$	$42.544$	\(\Q(\sqrt{-1}) \)	None					222.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{5}-3 q^{7}-3 q^{11}-i q^{13}+\cdots\)
5328.2.h.c	$5328$	$2$	5328.h	37.b	$2$	$2$	$2$	$42.544$	\(\Q(\sqrt{-1}) \)	None					37.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-3 q^{7}-3 q^{11}-3\beta q^{13}+\cdots\)
5328.2.h.d	$5328$	$2$	5328.h	37.b	$2$	$2$	$2$	$42.544$	\(\Q(\sqrt{-3}) \)	None					148.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{5}-q^{7}+3 q^{11}-\beta q^{13}+\beta q^{17}+\cdots\)
5328.2.h.e	$5328$	$2$	5328.h	37.b	$2$	$2$	$2$	$42.544$	\(\Q(\sqrt{-1}) \)	None					111.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-\beta q^{17}-3\beta q^{19}+2\beta q^{23}+\cdots\)
5328.2.h.f	$5328$	$2$	5328.h	37.b	$2$	$2$	$2$	$42.544$	\(\Q(\sqrt{-1}) \)	None					888.2.h.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 q^{11}-2\beta q^{13}-2\beta q^{17}-\beta q^{19}+\cdots\)
5328.2.h.g	$5328$	$2$	5328.h	37.b	$2$	$4$	$4$	$42.544$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None					444.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+(-1+\beta _{3})q^{7}+(-2+2\beta _{3})q^{11}+\cdots\)
5328.2.h.h	$5328$	$2$	5328.h	37.b	$2$	$4$	$4$	$42.544$	\(\Q(i, \sqrt{21})\)	None					666.2.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{7}-\beta _{3}q^{11}-\beta _{1}q^{13}-\beta _{2}q^{17}+\cdots\)
5328.2.h.i	$5328$	$2$	5328.h	37.b	$2$	$4$	$4$	$42.544$	\(\Q(i, \sqrt{65})\)	None					222.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(1-\beta _{3})q^{7}+(-1+\beta _{3})q^{11}+\cdots\)
5328.2.h.j	$5328$	$2$	5328.h	37.b	$2$	$4$	$4$	$42.544$	\(\Q(\sqrt{-5 + \sqrt{13}})\)	None					444.2.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(1-\beta _{2})q^{7}-2\beta _{1}q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)
5328.2.h.k	$5328$	$2$	5328.h	37.b	$2$	$4$	$4$	$42.544$	\(\Q(i, \sqrt{6})\)	None					1332.2.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+2q^{7}-\beta _{3}q^{11}-\beta _{2}q^{17}+\cdots\)
5328.2.h.l	$5328$	$2$	5328.h	37.b	$2$	$4$	$4$	$42.544$	\(\Q(\sqrt{-3 + \sqrt{6}})\)	None					111.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+2q^{7}-\beta _{3}q^{11}-2\beta _{2}q^{13}+\cdots\)
5328.2.h.m	$5328$	$2$	5328.h	37.b	$2$	$4$	$4$	$42.544$	\(\Q(i, \sqrt{21})\)	None					74.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+2q^{7}+(2-\beta _{3})q^{11}+\beta _{2}q^{13}+\cdots\)
5328.2.h.n	$5328$	$2$	5328.h	37.b	$2$	$6$	$6$	$42.544$	6.0.27206656.1	None					888.2.h.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
5328.2.h.o	$5328$	$2$	5328.h	37.b	$2$	$8$	$8$	$42.544$	8.0.\(\cdots\).1	\(\Q(\sqrt{-111}) \)					333.2.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{5}+\beta _{1}q^{7}+(\beta _{2}-\beta _{5})q^{17}-\beta _{4}q^{23}+\cdots\)
5328.2.h.p	$5328$	$2$	5328.h	37.b	$2$	$10$	$10$	$42.544$	10.0.\(\cdots\).1	None					888.2.h.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{3}q^{7}+(1-\beta _{1})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots\)
5328.2.h.q	$5328$	$2$	5328.h	37.b	$2$	$10$	$10$	$42.544$	10.0.\(\cdots\).1	None					296.2.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{5}+\beta _{3}q^{7}+\beta _{5}q^{11}+\beta _{4}q^{13}+\cdots\)
5328.2.h.r	$5328$	$2$	5328.h	37.b	$2$	$20$	$20$	$42.544$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None			✓		2664.2.h.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{5}-\beta _{1}q^{7}-\beta _{10}q^{11}+\beta _{12}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5328, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5328, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(888, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1332, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1776, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2664, [\chi])\)\(^{\oplus 2}\)