Space of modular forms of level 3264, weight 2, and Character 3264.c

• Label: 3264.2.c
• Level: $3264$
• Weight: $2$
• Character orbit: 3264.c
• Rep. character: $\chi_{3264}(577,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $18$
• Sturm bound: $1152$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 3264 = 2^{6} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3264.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1152\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(13\), \(19\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3264, [\chi])\).

	Total	New	Old
Modular forms	600	72	528
Cusp forms	552	72	480
Eisenstein series	48	0	48

Trace form

\( 72 q - 72 q^{9} - 8 q^{17} - 88 q^{25} - 72 q^{49} - 32 q^{69} + 96 q^{77} + 72 q^{81} - 32 q^{85} - 16 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3264, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3264.2.c.a	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					204.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}-2 i q^{7}-q^{9}+3 i q^{11}+\cdots\)
3264.2.c.b	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					204.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+i q^{5}+2 i q^{7}-q^{9}-3 i q^{11}+\cdots\)
3264.2.c.c	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					1632.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 i q^{5}-2 i q^{7}-q^{9}-2 q^{13}+\cdots\)
3264.2.c.d	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					51.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-4 i q^{7}-q^{9}-4 i q^{11}+\cdots\)
3264.2.c.e	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					51.2.d.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}-4 i q^{7}-q^{9}-4 i q^{11}+\cdots\)
3264.2.c.f	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					1632.2.c.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 i q^{5}+2 i q^{7}-q^{9}-2 q^{13}+\cdots\)
3264.2.c.g	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					51.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+3 i q^{5}-2 i q^{7}-q^{9}-5 i q^{11}+\cdots\)
3264.2.c.h	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					51.2.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+3 i q^{5}+2 i q^{7}-q^{9}+5 i q^{11}+\cdots\)
3264.2.c.i	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					102.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 i q^{5}-2 i q^{7}-q^{9}+6 q^{13}+\cdots\)
3264.2.c.j	$3264$	$2$	3264.c	17.b	$2$	$2$	$2$	$26.063$	\(\Q(\sqrt{-1}) \)	None					102.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 i q^{5}+2 i q^{7}-q^{9}+6 q^{13}+\cdots\)
3264.2.c.k	$3264$	$2$	3264.c	17.b	$2$	$4$	$4$	$26.063$	\(\Q(i, \sqrt{33})\)	None					408.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{2}q^{7}-q^{9}+\cdots\)
3264.2.c.l	$3264$	$2$	3264.c	17.b	$2$	$4$	$4$	$26.063$	\(\Q(i, \sqrt{33})\)	None					408.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{5}+2\beta _{2}q^{7}-q^{9}+\cdots\)
3264.2.c.m	$3264$	$2$	3264.c	17.b	$2$	$4$	$4$	$26.063$	\(\Q(i, \sqrt{13})\)	None					1632.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}-4\beta _{1}q^{7}-q^{9}+3\beta _{1}q^{11}+\cdots\)
3264.2.c.n	$3264$	$2$	3264.c	17.b	$2$	$6$	$6$	$26.063$	6.0.399424.1	None					408.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
3264.2.c.o	$3264$	$2$	3264.c	17.b	$2$	$6$	$6$	$26.063$	6.0.399424.1	None					408.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(\beta _{2}-\beta _{3}+\beta _{5})q^{7}+\cdots\)
3264.2.c.p	$3264$	$2$	3264.c	17.b	$2$	$8$	$8$	$26.063$	8.0.\(\cdots\).3	None					1632.2.c.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}-q^{9}+(3\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots\)
3264.2.c.q	$3264$	$2$	3264.c	17.b	$2$	$10$	$10$	$26.063$	10.0.\(\cdots\).1	None					1632.2.c.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+\beta _{9}q^{5}+\beta _{3}q^{7}-q^{9}+(\beta _{6}+\cdots)q^{11}+\cdots\)
3264.2.c.r	$3264$	$2$	3264.c	17.b	$2$	$10$	$10$	$26.063$	10.0.\(\cdots\).1	None					1632.2.c.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{9}q^{5}-\beta _{3}q^{7}-q^{9}+(-\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3264, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3264, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(816, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1088, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1632, [\chi])\)\(^{\oplus 2}\)