Space of modular forms of level 2640, weight 2, and Character 2640.d

• Label: 2640.2.d
• Level: $2640$
• Weight: $2$
• Character orbit: 2640.d
• Rep. character: $\chi_{2640}(529,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $11$
• Sturm bound: $1152$
• Trace bound: $21$

Defining parameters

Level:	\( N \)	\(=\)	\( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2640.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(1152\)
Trace bound:			\(21\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2640, [\chi])\).

	Total	New	Old
Modular forms	600	60	540
Cusp forms	552	60	492
Eisenstein series	48	0	48

Trace form

\( 60 q - 4 q^{5} - 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2640, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2640.2.d.a	$2640$	$2$	2640.d	5.b	$2$	$2$	$2$	$21.081$	\(\Q(\sqrt{-1}) \)	None					660.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-2 i-1)q^{5}+2 i q^{7}+\cdots\)
2640.2.d.b	$2640$	$2$	2640.d	5.b	$2$	$2$	$2$	$21.081$	\(\Q(\sqrt{-1}) \)	None					660.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+(-2 i+1)q^{5}-q^{9}-q^{11}+\cdots\)
2640.2.d.c	$2640$	$2$	2640.d	5.b	$2$	$4$	$4$	$21.081$	\(\Q(i, \sqrt{10})\)	None					330.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
2640.2.d.d	$2640$	$2$	2640.d	5.b	$2$	$4$	$4$	$21.081$	\(\Q(i, \sqrt{5})\)	None					660.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2640.2.d.e	$2640$	$2$	2640.d	5.b	$2$	$4$	$4$	$21.081$	\(\Q(\zeta_{8})\)	None					330.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{3}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
2640.2.d.f	$2640$	$2$	2640.d	5.b	$2$	$6$	$6$	$21.081$	6.0.350464.1	None					1320.2.d.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
2640.2.d.g	$2640$	$2$	2640.d	5.b	$2$	$6$	$6$	$21.081$	6.0.350464.1	None					1320.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(\beta _{1}+\beta _{5})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots\)
2640.2.d.h	$2640$	$2$	2640.d	5.b	$2$	$6$	$6$	$21.081$	6.0.350464.1	None					165.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
2640.2.d.i	$2640$	$2$	2640.d	5.b	$2$	$6$	$6$	$21.081$	6.0.350464.1	None					165.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(\beta _{1}+3\beta _{4}+\cdots)q^{7}+\cdots\)
2640.2.d.j	$2640$	$2$	2640.d	5.b	$2$	$10$	$10$	$21.081$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					1320.2.d.d	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{2}q^{5}-\beta _{9}q^{7}-q^{9}-q^{11}+\cdots\)
2640.2.d.k	$2640$	$2$	2640.d	5.b	$2$	$10$	$10$	$21.081$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					1320.2.d.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{5}q^{5}-\beta _{1}q^{7}-q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2640, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 2}\)