Space of modular forms of level 912, weight 2, and Character 912.f

• Label: 912.2.f
• Level: $912$
• Weight: $2$
• Character orbit: 912.f
• Rep. character: $\chi_{912}(113,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $9$
• Sturm bound: $320$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(320\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

	Total	New	Old
Modular forms	172	42	130
Cusp forms	148	38	110
Eisenstein series	24	4	20

Trace form

\( 38 q + 8 q^{7} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
912.2.f.a	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	\(\Q(\sqrt{-3}) \)	None					114.2.b.b	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-q^{7}+\cdots\)
912.2.f.b	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	\(\Q(\sqrt{-2}) \)	None					114.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta )q^{3}+\beta q^{5}+4q^{7}+(-1+\cdots)q^{9}+\cdots\)
912.2.f.c	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)					228.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{6}q^{3}-4q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
912.2.f.d	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	\(\Q(\sqrt{-2}) \)	None					114.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta )q^{3}+\beta q^{5}+4q^{7}+(-1-2\beta )q^{9}+\cdots\)
912.2.f.e	$912$	$2$	912.f	57.d	$2$	$2$	$2$	$7.282$	\(\Q(\sqrt{-3}) \)	None					114.2.b.b	$2$	$0$	\(0\)	\(3\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{6})q^{3}+(2-4\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}+\cdots\)
912.2.f.f	$912$	$2$	912.f	57.d	$2$	$4$	$4$	$7.282$	\(\Q(\sqrt{2}, \sqrt{-5})\)	None					57.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{2})q^{3}-\beta _{3}q^{5}-q^{7}+(-2+\cdots)q^{9}+\cdots\)
912.2.f.g	$912$	$2$	912.f	57.d	$2$	$4$	$4$	$7.282$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	None					228.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+q^{7}+(2-\beta _{2})q^{9}+\cdots\)
912.2.f.h	$912$	$2$	912.f	57.d	$2$	$10$	$10$	$7.282$	10.0.\(\cdots\).1	None					456.2.f.a	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)
912.2.f.i	$912$	$2$	912.f	57.d	$2$	$10$	$10$	$7.282$	10.0.\(\cdots\).1	None					456.2.f.a	$2$	$0$	\(0\)	\(1\)	\(0\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(912, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)