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

• Label: 3264.2.l
• Level: $3264$
• Weight: $2$
• Character orbit: 3264.l
• Rep. character: $\chi_{3264}(2209,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $1152$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3264 = 2^{6} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3264.l (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1152\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(11\)

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

\( 72 q + 72 q^{9} + 24 q^{17} + 24 q^{25} - 72 q^{49} + 72 q^{81} - 48 q^{89}+O(q^{100}) \)

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.l.a	$3264$	$2$	3264.l	136.h	$2$	$4$	$4$	$26.063$	\(\Q(\zeta_{8})\)	None		✓			3264.2.l.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta_{2} q^{5}+q^{9}-4 q^{11}+\beta_{2} q^{15}+\cdots\)
3264.2.l.b	$3264$	$2$	3264.l	136.h	$2$	$4$	$4$	$26.063$	\(\Q(\zeta_{8})\)	None		✓			3264.2.l.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta_{2} q^{5}+q^{9}+4 q^{11}-\beta_{2} q^{15}+\cdots\)
3264.2.l.c	$3264$	$2$	3264.l	136.h	$2$	$8$	$8$	$26.063$	8.0.303595776.1	None		✓			3264.2.l.c	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{6})q^{7}+q^{9}+\cdots\)
3264.2.l.d	$3264$	$2$	3264.l	136.h	$2$	$8$	$8$	$26.063$	8.0.303595776.1	None		✓			3264.2.l.c	$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{2}q^{5}+(-\beta _{1}-\beta _{6})q^{7}+q^{9}+\cdots\)
3264.2.l.e	$3264$	$2$	3264.l	136.h	$2$	$24$	$24$	$26.063$		None		✓			3264.2.l.e	$4$	$0$	\(0\)	\(-24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
3264.2.l.f	$3264$	$2$	3264.l	136.h	$2$	$24$	$24$	$26.063$		None		✓			3264.2.l.e	$4$	$0$	\(0\)	\(24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(3264, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1088, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1632, [\chi])\)\(^{\oplus 2}\)