Space of modular forms of level 3640, weight 2, and Character 3640.w

• Label: 3640.2.w
• Level: $3640$
• Weight: $2$
• Character orbit: 3640.w
• Rep. character: $\chi_{3640}(2521,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $16$
• Sturm bound: $1344$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3640.w (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(1344\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3640, [\chi])\).

	Total	New	Old
Modular forms	688	84	604
Cusp forms	656	84	572
Eisenstein series	32	0	32

Trace form

\( 84 q + 84 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3640, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3640.2.w.a	$3640$	$2$	3640.w	13.b	$2$	$2$	$2$	$29.066$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}-iq^{5}+iq^{7}+6q^{9}+3iq^{11}+\cdots\)
3640.2.w.b	$3640$	$2$	3640.w	13.b	$2$	$2$	$2$	$29.066$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}+iq^{5}-iq^{7}+q^{9}+(-2-3i)q^{13}+\cdots\)
3640.2.w.c	$3640$	$2$	3640.w	13.b	$2$	$2$	$2$	$29.066$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}+iq^{5}-iq^{7}+q^{9}+6iq^{11}+\cdots\)
3640.2.w.d	$3640$	$2$	3640.w	13.b	$2$	$2$	$2$	$29.066$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}+iq^{5}+iq^{7}+q^{9}-4iq^{11}+\cdots\)
3640.2.w.e	$3640$	$2$	3640.w	13.b	$2$	$2$	$2$	$29.066$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}-iq^{5}-iq^{7}+q^{9}-2iq^{11}+\cdots\)
3640.2.w.f	$3640$	$2$	3640.w	13.b	$2$	$2$	$2$	$29.066$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{5}+iq^{7}-3q^{9}+(-2-3i)q^{13}+\cdots\)
3640.2.w.g	$3640$	$2$	3640.w	13.b	$2$	$2$	$2$	$29.066$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{3}+iq^{5}-iq^{7}+q^{9}+2iq^{11}+\cdots\)
3640.2.w.h	$3640$	$2$	3640.w	13.b	$2$	$2$	$2$	$29.066$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{3}+iq^{5}+iq^{7}+q^{9}-4iq^{11}+\cdots\)
3640.2.w.i	$3640$	$2$	3640.w	13.b	$2$	$4$	$4$	$29.066$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+\beta _{2}q^{7}+(2+\cdots)q^{9}+\cdots\)
3640.2.w.j	$3640$	$2$	3640.w	13.b	$2$	$4$	$4$	$29.066$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2})q^{3}-\beta _{3}q^{5}+\beta _{3}q^{7}+(-1+\cdots)q^{9}+\cdots\)
3640.2.w.k	$3640$	$2$	3640.w	13.b	$2$	$4$	$4$	$29.066$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}+\beta _{2}q^{5}-\beta _{2}q^{7}+(1-\beta _{3})q^{9}+\cdots\)
3640.2.w.l	$3640$	$2$	3640.w	13.b	$2$	$6$	$6$	$29.066$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}+\beta _{3}q^{7}+(2\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
3640.2.w.m	$3640$	$2$	3640.w	13.b	$2$	$6$	$6$	$29.066$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{4})q^{3}-\beta _{3}q^{5}+\beta _{3}q^{7}+(1-\beta _{2}+\cdots)q^{9}+\cdots\)
3640.2.w.n	$3640$	$2$	3640.w	13.b	$2$	$8$	$8$	$29.066$	8.0.6179217664.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{5})q^{3}-\beta _{6}q^{5}+\beta _{6}q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
3640.2.w.o	$3640$	$2$	3640.w	13.b	$2$	$12$	$12$	$29.066$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{4}q^{5}-\beta _{4}q^{7}+(-\beta _{3}-\beta _{6}+\cdots)q^{9}+\cdots\)
3640.2.w.p	$3640$	$2$	3640.w	13.b	$2$	$24$	$24$	$29.066$		None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3640, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3640, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(910, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1820, [\chi])\)\(^{\oplus 2}\)