Space of modular forms of level 3648, weight 2, and Character 3648.k

• Label: 3648.2.k
• Level: $3648$
• Weight: $2$
• Character orbit: 3648.k
• Rep. character: $\chi_{3648}(2431,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $12$
• Sturm bound: $1280$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3648.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1280\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3648, [\chi])\).

	Total	New	Old
Modular forms	664	80	584
Cusp forms	616	80	536
Eisenstein series	48	0	48

Trace form

\( 80 q + 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3648, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3648.2.k.a	$3648$	$2$	3648.k	76.d	$2$	$2$	$2$	$29.129$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(-6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-3q^{5}+\zeta_{6}q^{7}+q^{9}+3\zeta_{6}q^{11}+\cdots\)
3648.2.k.b	$3648$	$2$	3648.k	76.d	$2$	$2$	$2$	$29.129$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-2\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{11}+2\zeta_{6}q^{13}+\cdots\)
3648.2.k.c	$3648$	$2$	3648.k	76.d	$2$	$2$	$2$	$29.129$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2q^{5}+2\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
3648.2.k.d	$3648$	$2$	3648.k	76.d	$2$	$2$	$2$	$29.129$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(2\)	\(-6\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-3q^{5}+\zeta_{6}q^{7}+q^{9}+3\zeta_{6}q^{11}+\cdots\)
3648.2.k.e	$3648$	$2$	3648.k	76.d	$2$	$2$	$2$	$29.129$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-2\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots\)
3648.2.k.f	$3648$	$2$	3648.k	76.d	$2$	$2$	$2$	$29.129$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+2q^{5}+2\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
3648.2.k.g	$3648$	$2$	3648.k	76.d	$2$	$4$	$4$	$29.129$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-4\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{3}q^{5}+\beta _{1}q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
3648.2.k.h	$3648$	$2$	3648.k	76.d	$2$	$4$	$4$	$29.129$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(4\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{3}q^{5}-\beta _{1}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
3648.2.k.i	$3648$	$2$	3648.k	76.d	$2$	$10$	$10$	$29.129$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-10\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{1}q^{5}+\beta _{5}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
3648.2.k.j	$3648$	$2$	3648.k	76.d	$2$	$10$	$10$	$29.129$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(10\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{1}q^{5}-\beta _{5}q^{7}+q^{9}+(\beta _{2}+\beta _{8}+\cdots)q^{11}+\cdots\)
3648.2.k.k	$3648$	$2$	3648.k	76.d	$2$	$20$	$20$	$29.129$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(-20\)	\(0\)	\(0\)	$2^{27}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{5}q^{5}+\beta _{17}q^{7}+q^{9}+\beta _{6}q^{11}+\cdots\)
3648.2.k.l	$3648$	$2$	3648.k	76.d	$2$	$20$	$20$	$29.129$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(20\)	\(0\)	\(0\)	$2^{27}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{5}q^{5}-\beta _{17}q^{7}+q^{9}-\beta _{6}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3648, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \)