Space of modular forms of level 3872, weight 2, and Character 3872.g

• Label: 3872.2.g
• Level: $3872$
• Weight: $2$
• Character orbit: 3872.g
• Rep. character: $\chi_{3872}(1935,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $5$
• Sturm bound: $1056$
• Trace bound: $3$

Defining parameters

Level:	$N$	$=$	$3872 = 2^{5} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3872.g (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$88$
Character field:			$\Q$
Newform subspaces:			$5$
Sturm bound:			$1056$
Trace bound:			$3$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3872, [\chi])$.

	Total	New	Old
Modular forms	576	116	460
Cusp forms	480	100	380
Eisenstein series	96	16	80

Trace form

$100 q - 4 q^{3} + 88 q^{9} - 64 q^{25} - 16 q^{27} + 56 q^{49} - 36 q^{59} + 56 q^{67} + 96 q^{75} + 60 q^{81} - 16 q^{89} + 48 q^{91} - 12 q^{97}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(3872, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3872.2.g.a	$3872$	$2$	3872.g	88.g	$2$	$8$	$8$	$30.918$	$\Q(\zeta_{24})$	None					968.2.g.b	$4$	$0$	$0$	$-8$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta_{4}-1)q^{3}+(\beta_{2}+2\beta_1)q^{5}+\cdots$
3872.2.g.b	$3872$	$2$	3872.g	88.g	$2$	$8$	$8$	$30.918$	8.0.64000000.1	$\Q(\sqrt{-2})$					88.2.k.a	$4$	$0$	$0$	$4$	$0$	$0$	$2^{4}\cdot 11^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{3}+(4+\beta _{6})q^{9}+(\beta _{1}+\beta _{3}-\beta _{5}+\cdots)q^{17}+\cdots$
3872.2.g.c	$3872$	$2$	3872.g	88.g	$2$	$20$	$20$	$30.918$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None					968.2.g.c	$4$	$0$	$0$	$0$	$0$	$0$	$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}-\beta _{6}q^{5}+\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$
3872.2.g.d	$3872$	$2$	3872.g	88.g	$2$	$32$	$32$	$30.918$		None					88.2.k.b	$4$	$0$	$0$	$-8$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
3872.2.g.e	$3872$	$2$	3872.g	88.g	$2$	$32$	$32$	$30.918$		None					968.2.g.d	$4$	$0$	$0$	$8$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$

Decomposition of $S_{2}^{\mathrm{old}}(3872, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3872, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(88, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(352, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(968, [\chi])$$^{\oplus 3}$