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

• Label: 3276.2.h
• Level: $3276$
• Weight: $2$
• Character orbit: 3276.h
• Rep. character: $\chi_{3276}(1637,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $1344$
• Trace bound: $25$

Defining parameters

Level:	$N$	$=$	$3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3276.h (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$273$
Character field:			$\Q$
Newform subspaces:			$3$
Sturm bound:			$1344$
Trace bound:			$25$
Distinguishing $T_p$:			$5$

Dimensions

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

	Total	New	Old
Modular forms	696	40	656
Cusp forms	648	40	608
Eisenstein series	48	0	48

Trace form

$40 q - 56 q^{25} + 16 q^{49}+O(q^{100})$

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.h.a	$3276$	$2$	3276.h	273.g	$2$	$8$	$8$	$26.159$	8.0.1871773696.1	None		✓			3276.2.h.a	$8$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{4}q^{13}-\beta _{7}q^{17}+\cdots$
3276.2.h.b	$3276$	$2$	3276.h	273.g	$2$	$16$	$16$	$26.159$	16.0.$\cdots$.13	$\Q(\sqrt{-91})$		✓			3276.2.h.b	$8$	$0$	$0$	$0$	$0$	$0$	$2^{10}\cdot 3^{8}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{7}q^{5}+\beta _{2}q^{7}-\beta _{6}q^{13}-\beta _{5}q^{19}+\cdots$
3276.2.h.c	$3276$	$2$	3276.h	273.g	$2$	$16$	$16$	$26.159$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			3276.2.h.c	$8$	$0$	$0$	$0$	$0$	$0$	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{11}q^{5}+\beta _{10}q^{7}+(\beta _{4}+\beta _{7})q^{11}+\cdots$

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

$S_{2}^{\mathrm{old}}(3276, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(273, [\chi])$$^{\oplus 6}$$\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}$