Space of modular forms of level 3276, weight 2, and Character 3276.gv

• Label: 3276.2.gv
• Level: $3276$
• Weight: $2$
• Character orbit: 3276.gv
• Rep. character: $\chi_{3276}(1117,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $92$
• Newform subspaces: $8$
• Sturm bound: $1344$
• Trace bound: $13$

Defining parameters

Level:	$N$	$=$	$3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3276.gv (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$91$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$8$
Sturm bound:			$1344$
Trace bound:			$13$
Distinguishing $T_p$:			$5$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3276, [\chi])$.

	Total	New	Old
Modular forms	1392	92	1300
Cusp forms	1296	92	1204
Eisenstein series	96	0	96

Trace form

$92 q - 4 q^{13} + 6 q^{17} - 10 q^{23} + 40 q^{25} - 14 q^{35} + 32 q^{43} - 20 q^{49} + 2 q^{53} + 4 q^{55} + 6 q^{61} + 28 q^{65} - 46 q^{77} + 38 q^{79} + 34 q^{91} - 30 q^{95}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(3276, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3276.2.gv.a	$3276$	$2$	3276.gv	91.r	$6$	$2$	$1$	$26.159$	$\Q(\sqrt{-3})$	$\Q(\sqrt{-3})$		✓			3276.2.gv.a	$4$	$0$	$0$	$0$	$0$	$-5$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-3+\zeta_{6})q^{7}+(-1-3\zeta_{6})q^{13}+\cdots$
3276.2.gv.b	$3276$	$2$	3276.gv	91.r	$6$	$2$	$1$	$26.159$	$\Q(\sqrt{-3})$	$\Q(\sqrt{-3})$		✓			3276.2.gv.a	$4$	$0$	$0$	$0$	$0$	$5$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+(3-\zeta_{6})q^{7}+(-4+3\zeta_{6})q^{13}+(-5+\cdots)q^{19}+\cdots$
3276.2.gv.c	$3276$	$2$	3276.gv	91.r	$6$	$4$	$2$	$26.159$	$\Q(\zeta_{12})$	None					1092.2.cu.a	$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+2\zeta_{12}q^{5}+(\zeta_{12}+2\zeta_{12}^{3})q^{7}+(\zeta_{12}+\cdots)q^{11}+\cdots$
3276.2.gv.d	$3276$	$2$	3276.gv	91.r	$6$	$8$	$4$	$26.159$	8.0.$\cdots$.8	None					364.2.y.a	$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{5}+\beta _{3}q^{7}+\cdots$
3276.2.gv.e	$3276$	$2$	3276.gv	91.r	$6$	$12$	$6$	$26.159$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					364.2.y.b	$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{7}-\beta _{8}-\beta _{9}-\beta _{11})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
3276.2.gv.f	$3276$	$2$	3276.gv	91.r	$6$	$12$	$6$	$26.159$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None					1092.2.cu.b	$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{4}q^{5}+(\beta _{6}+\beta _{11})q^{7}+(\beta _{1}-\beta _{6}+\cdots)q^{11}+\cdots$
3276.2.gv.g	$3276$	$2$	3276.gv	91.r	$6$	$20$	$10$	$26.159$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None					1092.2.cu.c	$4$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{13}q^{5}+(\beta _{1}+\beta _{17})q^{7}+\beta _{15}q^{11}+\cdots$
3276.2.gv.h	$3276$	$2$	3276.gv	91.r	$6$	$32$	$16$	$26.159$		None		✓	✓		3276.2.gv.h	$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$

Decomposition of $S_{2}^{\mathrm{old}}(3276, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3276, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(91, [\chi])$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(182, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(273, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(364, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(546, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(819, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(1092, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1638, [\chi])$$^{\oplus 2}$