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

$96 q - 96 q^{9} - 96 q^{25} + 96 q^{49} + 96 q^{81}+O(q^{100})$

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}$