Space of modular forms of level 3240, weight 2, and Character 3240.f

• Label: 3240.2.f
• Level: $3240$
• Weight: $2$
• Character orbit: 3240.f
• Rep. character: $\chi_{3240}(649,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $11$
• Sturm bound: $1296$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3240.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(1296\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3240, [\chi])\).

	Total	New	Old
Modular forms	696	72	624
Cusp forms	600	72	528
Eisenstein series	96	0	96

Trace form

\( 72 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3240, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3240.2.f.a	$3240$	$2$	3240.f	5.b	$2$	$2$	$2$	$25.872$	\(\Q(\sqrt{-1}) \)	None		✓			3240.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-2)q^{5}+5 i q^{7}+4 q^{11}+5 i q^{13}+\cdots\)
3240.2.f.b	$3240$	$2$	3240.f	5.b	$2$	$2$	$2$	$25.872$	\(\Q(\sqrt{-1}) \)	None					360.2.bi.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2 i-1)q^{5}+i q^{7}+2 q^{11}+\cdots\)
3240.2.f.c	$3240$	$2$	3240.f	5.b	$2$	$2$	$2$	$25.872$	\(\Q(\sqrt{-1}) \)	None		✓			3240.2.f.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta-1)q^{5}+\beta q^{7}+5 q^{11}-2\beta q^{13}+\cdots\)
3240.2.f.d	$3240$	$2$	3240.f	5.b	$2$	$2$	$2$	$25.872$	\(\Q(\sqrt{-1}) \)	None		✓			3240.2.f.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta+1)q^{5}+\beta q^{7}-5 q^{11}-2\beta q^{13}+\cdots\)
3240.2.f.e	$3240$	$2$	3240.f	5.b	$2$	$2$	$2$	$25.872$	\(\Q(\sqrt{-1}) \)	None					360.2.bi.a	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2 i+1)q^{5}+i q^{7}-2 q^{11}-2 i q^{13}+\cdots\)
3240.2.f.f	$3240$	$2$	3240.f	5.b	$2$	$2$	$2$	$25.872$	\(\Q(\sqrt{-1}) \)	None		✓			3240.2.f.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i+2)q^{5}+5 i q^{7}-4 q^{11}+\cdots\)
3240.2.f.g	$3240$	$2$	3240.f	5.b	$2$	$6$	$6$	$25.872$	6.0.29160000.2	None		✓			3240.2.f.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{5}q^{7}+(-1-\beta _{2}+\beta _{3}+\cdots)q^{11}+\cdots\)
3240.2.f.h	$3240$	$2$	3240.f	5.b	$2$	$6$	$6$	$25.872$	6.0.29160000.2	None		✓			3240.2.f.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}-\beta _{5}q^{7}+(1+\beta _{2}-\beta _{3})q^{11}+\cdots\)
3240.2.f.i	$3240$	$2$	3240.f	5.b	$2$	$16$	$16$	$25.872$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					360.2.bi.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}+\beta _{10}q^{7}+(1-\beta _{7})q^{11}-\beta _{5}q^{13}+\cdots\)
3240.2.f.j	$3240$	$2$	3240.f	5.b	$2$	$16$	$16$	$25.872$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			3240.2.f.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}-\beta _{1}q^{7}+\beta _{10}q^{11}-\beta _{2}q^{13}+\cdots\)
3240.2.f.k	$3240$	$2$	3240.f	5.b	$2$	$16$	$16$	$25.872$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					360.2.bi.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{10}q^{7}+(-1+\beta _{7})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3240, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1620, [\chi])\)\(^{\oplus 2}\)