Space of modular forms of level 3328, weight 2, and Character 3328.b

• Label: 3328.2.b
• Level: $3328$
• Weight: $2$
• Character orbit: 3328.b
• Rep. character: $\chi_{3328}(1665,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $30$
• Sturm bound: $896$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3328 = 2^{8} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3328.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 30 \)
Sturm bound:			\(896\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3328, [\chi])\).

	Total	New	Old
Modular forms	472	96	376
Cusp forms	424	96	328
Eisenstein series	48	0	48

Trace form

\( 96 q - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3328, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3328.2.b.a	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}-5q^{7}+2q^{9}+2iq^{11}+\cdots\)
3328.2.b.b	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-2iq^{5}-4q^{7}-q^{9}-6iq^{11}+\cdots\)
3328.2.b.c	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}-3q^{7}+2q^{9}-2iq^{11}+\cdots\)
3328.2.b.d	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-2iq^{5}-2q^{7}-q^{9}+iq^{13}+\cdots\)
3328.2.b.e	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{5}-2q^{7}+3q^{9}-2iq^{11}-iq^{13}+\cdots\)
3328.2.b.f	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+3iq^{5}-q^{7}-6q^{9}-4iq^{11}+\cdots\)
3328.2.b.g	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}-iq^{5}-q^{7}-6q^{9}-2iq^{11}+\cdots\)
3328.2.b.h	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}-q^{7}+2q^{9}+iq^{13}+\cdots\)
3328.2.b.i	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}-q^{7}+2q^{9}+4iq^{11}+\cdots\)
3328.2.b.j	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-3iq^{5}-q^{7}+2q^{9}-6iq^{11}+\cdots\)
3328.2.b.k	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+iq^{5}+q^{7}-6q^{9}-2iq^{11}+\cdots\)
3328.2.b.l	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}-3iq^{5}+q^{7}-6q^{9}-4iq^{11}+\cdots\)
3328.2.b.m	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+3iq^{5}+q^{7}+2q^{9}-6iq^{11}+\cdots\)
3328.2.b.n	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}+q^{7}+2q^{9}-iq^{13}+\cdots\)
3328.2.b.o	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}+q^{7}+2q^{9}+4iq^{11}+\cdots\)
3328.2.b.p	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+2iq^{5}+2q^{7}-q^{9}-iq^{13}+\cdots\)
3328.2.b.q	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2iq^{5}+2q^{7}+3q^{9}+2iq^{11}-iq^{13}+\cdots\)
3328.2.b.r	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}+3q^{7}+2q^{9}-2iq^{11}+\cdots\)
3328.2.b.s	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+2iq^{5}+4q^{7}-q^{9}-6iq^{11}+\cdots\)
3328.2.b.t	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}+5q^{7}+2q^{9}+2iq^{11}+\cdots\)
3328.2.b.u	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
3328.2.b.v	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(\zeta_{8}+2\zeta_{8}^{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
3328.2.b.w	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
3328.2.b.x	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+3\beta _{1}q^{5}+\beta _{3}q^{7}-2q^{9}+\cdots\)
3328.2.b.y	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(1-\beta _{3})q^{7}+\cdots\)
3328.2.b.z	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(-\zeta_{8}-2\zeta_{8}^{2})q^{5}+\cdots\)
3328.2.b.ba	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
3328.2.b.bb	$3328$	$2$	3328.b	8.b	$2$	$8$	$8$	$26.574$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(\beta _{2}+\beta _{5})q^{5}+(\beta _{4}-\beta _{7})q^{7}+\cdots\)
3328.2.b.bc	$3328$	$2$	3328.b	8.b	$2$	$10$	$10$	$26.574$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}+\beta _{1}q^{5}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
3328.2.b.bd	$3328$	$2$	3328.b	8.b	$2$	$10$	$10$	$26.574$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}-\beta _{1}q^{5}+(1-\beta _{4}-\beta _{5}+\beta _{7}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3328, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3328, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1664, [\chi])\)\(^{\oplus 2}\)