Space of modular forms of level 1632, weight 2, and Character 1632.c

• Label: 1632.2.c
• Level: $1632$
• Weight: $2$
• Character orbit: 1632.c
• Rep. character: $\chi_{1632}(577,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $6$
• Sturm bound: $576$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1632 = 2^{5} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1632.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1632, [\chi])\).

	Total	New	Old
Modular forms	304	36	268
Cusp forms	272	36	236
Eisenstein series	32	0	32

Trace form

\( 36 q - 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1632, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1632.2.c.a	$1632$	$2$	1632.c	17.b	$2$	$2$	$2$	$13.032$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{5}+2iq^{7}-q^{9}+2q^{13}+\cdots\)
1632.2.c.b	$1632$	$2$	1632.c	17.b	$2$	$2$	$2$	$13.032$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{5}-2iq^{7}-q^{9}+2q^{13}+\cdots\)
1632.2.c.c	$1632$	$2$	1632.c	17.b	$2$	$4$	$4$	$13.032$	\(\Q(i, \sqrt{13})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}-4\beta _{1}q^{7}-q^{9}-3\beta _{1}q^{11}+\cdots\)
1632.2.c.d	$1632$	$2$	1632.c	17.b	$2$	$8$	$8$	$13.032$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{3}q^{5}-q^{9}+(-3\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)
1632.2.c.e	$1632$	$2$	1632.c	17.b	$2$	$10$	$10$	$13.032$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+\beta _{9}q^{5}-\beta _{3}q^{7}-q^{9}+(\beta _{6}+\cdots)q^{11}+\cdots\)
1632.2.c.f	$1632$	$2$	1632.c	17.b	$2$	$10$	$10$	$13.032$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{9}q^{5}+\beta _{3}q^{7}-q^{9}+(-\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1632, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1632, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 6}\)