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

• Label: 4608.2.d
• Level: $4608$
• Weight: $2$
• Character orbit: 4608.d
• Rep. character: $\chi_{4608}(2305,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $18$
• Sturm bound: $1536$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 4608 = 2^{9} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4608.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1536\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	832	80	752
Cusp forms	704	80	624
Eisenstein series	128	0	128

Trace form

\( 80 q - 80 q^{25} + 80 q^{49} - 32 q^{65} + 32 q^{73} + 32 q^{89}+O(q^{100}) \)

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.d.a	$4608$	$2$	4608.d	8.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None					512.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}-4q^{7}+\beta q^{11}-2\beta q^{13}+\cdots\)
4608.2.d.b	$4608$	$2$	4608.d	8.b	$2$	$2$	$2$	$36.795$	\(\Q(\sqrt{-2}) \)	None					512.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+4q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
4608.2.d.c	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None					1536.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{5}+(-\beta_{3}-2)q^{7}+\cdots\)
4608.2.d.d	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					512.2.a.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{3}q^{7}-\beta _{1}q^{11}+\beta _{2}q^{13}+\cdots\)
4608.2.d.e	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			4608.2.a.v	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}+2\beta _{2}q^{13}+\cdots\)
4608.2.d.f	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None					1536.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{5}+\beta_{3} q^{7}+(-2\beta_{2}+\beta_1)q^{11}+\cdots\)
4608.2.d.g	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None					1536.2.a.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}-\beta_{3} q^{7}+\beta_1 q^{11}-2 q^{17}+\cdots\)
4608.2.d.h	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None					1536.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{5}-\beta_{3} q^{7}+(2\beta_{2}-\beta_1)q^{11}+\cdots\)
4608.2.d.i	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		✓			4608.2.a.x	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}-\beta _{3}q^{13}+\cdots\)
4608.2.d.j	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None					512.2.a.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}+\beta_{3} q^{7}+3\beta_{2} q^{11}+3\beta_1 q^{13}+\cdots\)
4608.2.d.k	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-2}) \)					512.2.a.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta_{2} q^{11}-\beta_{3} q^{17}+(-\beta_{2}-2\beta_1)q^{19}+\cdots\)
4608.2.d.l	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None		✓			4608.2.a.x	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+\beta _{3}q^{13}+\cdots\)
4608.2.d.m	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			4608.2.a.v	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-2\beta _{2}q^{13}+\cdots\)
4608.2.d.n	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None					1536.2.a.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}-3\beta_{3} q^{7}+3\beta_1 q^{11}+4\beta_{2} q^{13}+\cdots\)
4608.2.d.o	$4608$	$2$	4608.d	8.b	$2$	$4$	$4$	$36.795$	\(\Q(\zeta_{8})\)	None					1536.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{5}+(\beta_{3}+2)q^{7}+\cdots\)
4608.2.d.p	$4608$	$2$	4608.d	8.b	$2$	$8$	$8$	$36.795$	8.0.18939904.2	None					1536.2.a.m	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{5}-\beta _{2}q^{7}+(-\beta _{4}+\beta _{6})q^{11}+\cdots\)
4608.2.d.q	$4608$	$2$	4608.d	8.b	$2$	$8$	$8$	$36.795$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-6}) \)		✓			4608.2.a.s	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_{5} q^{5}-\beta_{3} q^{7}+\beta_1 q^{11}+(\beta_{6}-5)q^{25}+\cdots\)
4608.2.d.r	$4608$	$2$	4608.d	8.b	$2$	$8$	$8$	$36.795$	\(\Q(\zeta_{24})\)	None		✓			4608.2.a.u	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{5}+\beta_{7} q^{7}-\beta_1 q^{11}-\beta_{4} q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4608, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2304, [\chi])\)\(^{\oplus 2}\)