Space of modular forms of level 3300, weight 2, and Character 3300.c

• Label: 3300.2.c
• Level: $3300$
• Weight: $2$
• Character orbit: 3300.c
• Rep. character: $\chi_{3300}(1849,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $13$
• Sturm bound: $1440$
• Trace bound: $21$

Defining parameters

Level:	\( N \)	\(=\)	\( 3300 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3300.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(1440\)
Trace bound:			\(21\)
Distinguishing \(T_p\):			\(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3300, [\chi])\).

	Total	New	Old
Modular forms	756	32	724
Cusp forms	684	32	652
Eisenstein series	72	0	72

Trace form

\( 32 q - 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3300, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3300.2.c.a	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}-q^{11}-4iq^{13}+\cdots\)
3300.2.c.b	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+4iq^{7}-q^{9}-q^{11}-4iq^{13}+\cdots\)
3300.2.c.c	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}-q^{11}-6iq^{13}+\cdots\)
3300.2.c.d	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}-q^{11}+2iq^{13}+\cdots\)
3300.2.c.e	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{7}-q^{9}-q^{11}+iq^{13}+\cdots\)
3300.2.c.f	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+3iq^{7}-q^{9}-q^{11}-4iq^{13}+\cdots\)
3300.2.c.g	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+5iq^{7}-q^{9}+q^{11}-4iq^{13}+\cdots\)
3300.2.c.h	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}-q^{9}+q^{11}-4iq^{13}+2iq^{17}+\cdots\)
3300.2.c.i	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2iq^{7}-q^{9}+q^{11}-2iq^{13}+\cdots\)
3300.2.c.j	$3300$	$2$	3300.c	5.b	$2$	$2$	$2$	$26.351$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}-q^{9}+q^{11}-2iq^{13}+\cdots\)
3300.2.c.k	$3300$	$2$	3300.c	5.b	$2$	$4$	$4$	$26.351$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}-q^{9}-q^{11}+\cdots\)
3300.2.c.l	$3300$	$2$	3300.c	5.b	$2$	$4$	$4$	$26.351$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}-q^{9}+q^{11}+\cdots\)
3300.2.c.m	$3300$	$2$	3300.c	5.b	$2$	$4$	$4$	$26.351$	\(\Q(i, \sqrt{145})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-3\beta _{2}q^{7}-q^{9}+q^{11}-\beta _{1}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)