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

• Label: 4608.2.f
• Level: $4608$
• Weight: $2$
• Character orbit: 4608.f
• Rep. character: $\chi_{4608}(2303,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $16$
• Sturm bound: $1536$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 4608 = 2^{9} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4608.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(1536\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\), \(19\), \(23\)

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

\( 64 q + 64 q^{25} - 64 q^{49}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4608.2.f.a	$4608$	$2$	4608.f	24.f	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		✓			4608.2.c.l	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{5}+3\beta q^{7}+2\beta q^{11}+4\beta q^{13}+\cdots\)
4608.2.f.b	$4608$	$2$	4608.f	24.f	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		✓			4608.2.c.k	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{5}+\beta q^{7}-2\beta q^{11}+3\beta q^{17}+\cdots\)
4608.2.f.c	$4608$	$2$	4608.f	24.f	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		✓			4608.2.c.k	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{5}-\beta q^{7}+2\beta q^{11}+3\beta q^{17}+\cdots\)
4608.2.f.d	$4608$	$2$	4608.f	24.f	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		✓			4608.2.c.l	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{5}+3\beta q^{7}+2\beta q^{11}-4\beta q^{13}+\cdots\)
4608.2.f.e	$4608$	$2$	4608.f	24.f	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		✓			4608.2.c.l	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}-3\beta q^{7}+2\beta q^{11}-4\beta q^{13}+\cdots\)
4608.2.f.f	$4608$	$2$	4608.f	24.f	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		✓			4608.2.c.k	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}+\beta q^{7}+2\beta q^{11}+3\beta q^{17}+\cdots\)
4608.2.f.g	$4608$	$2$	4608.f	24.f	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		✓			4608.2.c.k	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}-\beta q^{7}-2\beta q^{11}+3\beta q^{17}+\cdots\)
4608.2.f.h	$4608$	$2$	4608.f	24.f	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None		✓			4608.2.c.l	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}+3\beta q^{7}-2\beta q^{11}-4\beta q^{13}+\cdots\)
4608.2.f.i	$4608$	$2$	4608.f	24.f	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None		✓			4608.2.c.a	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta_{2} q^{7}+2\beta_1 q^{11}-3\beta_1 q^{13}+\cdots\)
4608.2.f.j	$4608$	$2$	4608.f	24.f	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None		✓			4608.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{5}+\beta_{2} q^{7}-\beta_1 q^{13}-\beta_{2} q^{17}+\cdots\)
4608.2.f.k	$4608$	$2$	4608.f	24.f	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None		✓			4608.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3\beta_{2} q^{7}-2\beta_1 q^{11}-3\beta_1 q^{13}+\cdots\)
4608.2.f.l	$4608$	$2$	4608.f	24.f	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None		✓			4608.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{5}-\beta_{2} q^{7}-\beta_1 q^{13}-\beta_{2} q^{17}+\cdots\)
4608.2.f.m	$4608$	$2$	4608.f	24.f	$2$	$8$	$8$	$36.795$	\(\Q(\zeta_{24})\)	None		✓			4608.2.c.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{6} q^{5}-\beta_{7} q^{7}+(-\beta_{4}+\beta_1)q^{11}+\cdots\)
4608.2.f.n	$4608$	$2$	4608.f	24.f	$2$	$8$	$8$	$36.795$	\(\Q(\zeta_{16})\)	None		✓			4608.2.c.q	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{5}+(\beta_{2}+\beta_1)q^{7}+\beta_{4} q^{11}+\cdots\)
4608.2.f.o	$4608$	$2$	4608.f	24.f	$2$	$8$	$8$	$36.795$	\(\Q(\zeta_{16})\)	None		✓			4608.2.c.q	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{5}+(\beta_{2}+\beta_1)q^{7}+\beta_{4} q^{11}+\cdots\)
4608.2.f.p	$4608$	$2$	4608.f	24.f	$2$	$8$	$8$	$36.795$	\(\Q(\zeta_{24})\)	None		✓			4608.2.c.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{6} q^{5}-\beta_{7} q^{7}+(-\beta_{4}+\beta_1)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4608, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2304, [\chi])\)\(^{\oplus 2}\)