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

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