Space of modular forms of level 4608, weight 2, and Character 4608.c

• Label: 4608.2.c
• Level: $4608$
• Weight: $2$
• Character orbit: 4608.c
• Rep. character: $\chi_{4608}(4607,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $18$
• Sturm bound: $1536$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 4608 = 2^{9} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4608.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1536\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4608, [\chi])\).

	Total	New	Old
Modular forms	832	64	768
Cusp forms	704	64	640
Eisenstein series	128	0	128

Trace form

\( 64 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4608, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4608.2.c.a	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta q^{7}-4q^{11}-6q^{13}+3\beta q^{17}+\cdots\)
4608.2.c.b	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta q^{7}-4q^{11}+6q^{13}+3\beta q^{17}+\cdots\)
4608.2.c.c	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+\beta q^{7}-2q^{13}-\beta q^{17}-2\beta q^{19}+\cdots\)
4608.2.c.d	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}-\beta q^{7}-2q^{13}-\beta q^{17}+2\beta q^{19}+\cdots\)
4608.2.c.e	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}-\beta q^{7}+2q^{13}+\beta q^{17}-2\beta q^{19}+\cdots\)
4608.2.c.f	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+\beta q^{7}+2q^{13}+\beta q^{17}+2\beta q^{19}+\cdots\)
4608.2.c.g	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta q^{7}+4q^{11}-6q^{13}-3\beta q^{17}+\cdots\)
4608.2.c.h	$4608$	$2$	4608.c	12.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta q^{7}+4q^{11}+6q^{13}-3\beta q^{17}+\cdots\)
4608.2.c.i	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots\)
4608.2.c.j	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}+\beta _{2}q^{7}+(-2+\beta _{3})q^{11}+\cdots\)
4608.2.c.k	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}+3\zeta_{8}^{2}q^{17}+\cdots\)
4608.2.c.l	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{5}-3\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}-2\zeta_{8}^{3}q^{13}+\cdots\)
4608.2.c.m	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}-2\zeta_{8}^{3}q^{13}+\cdots\)
4608.2.c.n	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+3\zeta_{8}^{2}q^{17}+\cdots\)
4608.2.c.o	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+\cdots\)
4608.2.c.p	$4608$	$2$	4608.c	12.b	$2$	$4$	$4$	$36.795$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{5}-\beta _{2}q^{7}+(2-\beta _{3})q^{11}+\cdots\)
4608.2.c.q	$4608$	$2$	4608.c	12.b	$2$	$8$	$8$	$36.795$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}^{2}q^{5}+(-\zeta_{16}-\zeta_{16}^{3})q^{7}-\zeta_{16}^{5}q^{11}+\cdots\)
4608.2.c.r	$4608$	$2$	4608.c	12.b	$2$	$8$	$8$	$36.795$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{16}^{2}q^{5}+(-\zeta_{16}-\zeta_{16}^{3})q^{7}-\zeta_{16}^{5}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4608, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4608, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2304, [\chi])\)\(^{\oplus 2}\)