Space of modular forms of level 2112, weight 2, and Character 2112.h

• Label: 2112.2.h
• Level: $2112$
• Weight: $2$
• Character orbit: 2112.h
• Rep. character: $\chi_{2112}(1759,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $768$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2112.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 88 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(768\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\), \(59\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2112, [\chi])\).

	Total	New	Old
Modular forms	408	48	360
Cusp forms	360	48	312
Eisenstein series	48	0	48

Trace form

\( 48 q + 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2112, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2112.2.h.a	$2112$	$2$	2112.h	88.g	$2$	$8$	$8$	$16.864$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(-\zeta_{20}+\zeta_{20}^{2})q^{5}+\zeta_{20}^{5}q^{7}+\cdots\)
2112.2.h.b	$2112$	$2$	2112.h	88.g	$2$	$8$	$8$	$16.864$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(-\zeta_{20}+\zeta_{20}^{2})q^{5}-\zeta_{20}^{5}q^{7}+\cdots\)
2112.2.h.c	$2112$	$2$	2112.h	88.g	$2$	$16$	$16$	$16.864$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)	$2^{27}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{11}q^{5}+\beta _{2}q^{7}+q^{9}-\beta _{12}q^{11}+\cdots\)
2112.2.h.d	$2112$	$2$	2112.h	88.g	$2$	$16$	$16$	$16.864$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(16\)	\(0\)	\(0\)	$2^{27}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{11}q^{5}+\beta _{2}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2112, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1056, [\chi])\)\(^{\oplus 2}\)