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	Twist minimal	Largest	Maximal	Minimal twist	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					104.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}-5 q^{7}+2 q^{9}+2 i q^{11}+\cdots\)
3328.2.b.b	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}-2 i q^{5}-4 q^{7}-q^{9}-6 i q^{11}+\cdots\)
3328.2.b.c	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					416.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}-3 q^{7}+2 q^{9}-2 i q^{11}+\cdots\)
3328.2.b.d	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}-2 i q^{5}-2 q^{7}-q^{9}+i q^{13}+\cdots\)
3328.2.b.e	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					52.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 i q^{5}-2 q^{7}+3 q^{9}-2 i q^{11}+\cdots\)
3328.2.b.f	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+3 i q^{5}-q^{7}-6 q^{9}-4 i q^{11}+\cdots\)
3328.2.b.g	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					26.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-i q^{5}-q^{7}-6 q^{9}-2 i q^{11}+\cdots\)
3328.2.b.h	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.g	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}-q^{7}+2 q^{9}+i q^{13}+\cdots\)
3328.2.b.i	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}-q^{7}+2 q^{9}+4 i q^{11}+\cdots\)
3328.2.b.j	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					26.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-3 i q^{5}-q^{7}+2 q^{9}-6 i q^{11}+\cdots\)
3328.2.b.k	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					26.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+i q^{5}+q^{7}-6 q^{9}-2 i q^{11}+\cdots\)
3328.2.b.l	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-3 i q^{5}+q^{7}-6 q^{9}-4 i q^{11}+\cdots\)
3328.2.b.m	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					26.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+3 i q^{5}+q^{7}+2 q^{9}-6 i q^{11}+\cdots\)
3328.2.b.n	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}+q^{7}+2 q^{9}-i q^{13}+\cdots\)
3328.2.b.o	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}+q^{7}+2 q^{9}+4 i q^{11}+\cdots\)
3328.2.b.p	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+2 i q^{5}+2 q^{7}-q^{9}-i q^{13}+\cdots\)
3328.2.b.q	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					52.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 i q^{5}+2 q^{7}+3 q^{9}+2 i q^{11}+\cdots\)
3328.2.b.r	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					416.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}+3 q^{7}+2 q^{9}-2 i q^{11}+\cdots\)
3328.2.b.s	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					1664.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+2 i q^{5}+4 q^{7}-q^{9}-6 i q^{11}+\cdots\)
3328.2.b.t	$3328$	$2$	3328.b	8.b	$2$	$2$	$2$	$26.574$	\(\Q(\sqrt{-1}) \)	None					104.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-i q^{5}+5 q^{7}+2 q^{9}+2 i q^{11}+\cdots\)
3328.2.b.u	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{17})\)	None					416.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
3328.2.b.v	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(\zeta_{8})\)	None					1664.2.a.u	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{3}+(2\beta_{2}+\beta_1)q^{5}+\cdots\)
3328.2.b.w	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{17})\)	None					104.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-2\beta _{2})q^{5}+(-1+\beta _{3})q^{7}+\cdots\)
3328.2.b.x	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{5})\)	None					416.2.a.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+3\beta _{1}q^{5}+\beta _{3}q^{7}-2q^{9}+\cdots\)
3328.2.b.y	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{17})\)	None					104.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(1-\beta _{3})q^{7}+\cdots\)
3328.2.b.z	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(\zeta_{8})\)	None					1664.2.a.u	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{3}+(-2\beta_{2}-\beta_1)q^{5}+\cdots\)
3328.2.b.ba	$3328$	$2$	3328.b	8.b	$2$	$4$	$4$	$26.574$	\(\Q(i, \sqrt{17})\)	None					416.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+2\beta _{2})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
3328.2.b.bb	$3328$	$2$	3328.b	8.b	$2$	$8$	$8$	$26.574$	8.0.\(\cdots\).3	None					416.2.a.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(\beta _{2}+\beta _{5})q^{5}+(\beta _{4}-\beta _{7})q^{7}+\cdots\)
3328.2.b.bc	$3328$	$2$	3328.b	8.b	$2$	$10$	$10$	$26.574$	10.0.\(\cdots\).1	None					1664.2.a.y	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}+\beta _{1}q^{5}+(-1+\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
3328.2.b.bd	$3328$	$2$	3328.b	8.b	$2$	$10$	$10$	$26.574$	10.0.\(\cdots\).1	None					1664.2.a.y	$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}-\beta _{1}q^{5}+(1-\beta _{4}-\beta _{5}+\beta _{7}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3328, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1664, [\chi])\)\(^{\oplus 2}\)