Space of modular forms of level 756, weight 2, and Character 756.i

• Label: 756.2.i
• Level: $756$
• Weight: $2$
• Character orbit: 756.i
• Rep. character: $\chi_{756}(37,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$756 = 2^{2} \cdot 3^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	756.i (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$63$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$2$
Sturm bound:			$288$
Trace bound:			$1$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(756, [\chi])$.

	Total	New	Old
Modular forms	324	16	308
Cusp forms	252	16	236
Eisenstein series	72	0	72

Trace form

16 * q + 4 * q^5 + q^7 + 2 * q^11 - q^13 + 5 * q^17 + 2 * q^19 - 7 * q^23 - 8 * q^25 - 2 * q^29 - 4 * q^31 + 11 * q^35 - q^37 + 24 * q^41 + 2 * q^43 - 12 * q^47 + 7 * q^49 + 18 * q^53 - 12 * q^55 - 14 * q^59 + 26 * q^61 + 18 * q^65 + 14 * q^67 + 14 * q^71 + 14 * q^73 + 43 * q^77 + 2 * q^79 + 26 * q^83 - 6 * q^85 + 21 * q^89 + 5 * q^91 - 76 * q^95 - q^97

Decomposition of $S_{2}^{\mathrm{new}}(756, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
756.2.i.a	$756$	$2$	756.i	63.h	$3$	$2$	$1$	$6.037$	$\Q(\sqrt{-3})$	None					252.2.i.a	$2$	$0$	$0$	$0$	$2$	$-5$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+4\zeta_{6}q^{11}+\cdots$
756.2.i.b	$756$	$2$	756.i	63.h	$3$	$14$	$7$	$6.037$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None			✓		252.2.i.b	$2$	$0$	$0$	$0$	$2$	$6$	$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{5}+(\beta _{5}+\beta _{12})q^{7}+\beta _{13}q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(756, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(756, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(63, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(126, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(189, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(252, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(378, [\chi])$$^{\oplus 2}$