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

• Label: 912.2.cc
• Level: $912$
• Weight: $2$
• Character orbit: 912.cc
• Rep. character: $\chi_{912}(257,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $228$
• Newform subspaces: $8$
• Sturm bound: $320$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.cc (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(320\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	1032	252	780
Cusp forms	888	228	660
Eisenstein series	144	24	120

Trace form

\( 228 q + 6 q^{3} + 6 q^{7} - 12 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
912.2.cc.a	$912$	$2$	912.cc	57.j	$18$	$6$	$1$	$7.282$	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{18}]$	\(q+(\zeta_{18}^{2}-2\zeta_{18}^{5})q^{3}+(3\zeta_{18}-2\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
912.2.cc.b	$912$	$2$	912.cc	57.j	$18$	$6$	$1$	$7.282$	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{18}]$	\(q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+(\zeta_{18}+2\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
912.2.cc.c	$912$	$2$	912.cc	57.j	$18$	$18$	$3$	$7.282$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\beta _{12}q^{3}+(-\beta _{2}-\beta _{14}+\beta _{15})q^{5}+\cdots\)
912.2.cc.d	$912$	$2$	912.cc	57.j	$18$	$18$	$3$	$7.282$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\beta _{14}q^{3}+(-\beta _{9}+\beta _{17})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
912.2.cc.e	$912$	$2$	912.cc	57.j	$18$	$24$	$4$	$7.282$		None		$4$	$0$	\(0\)	\(9\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{18}]$
912.2.cc.f	$912$	$2$	912.cc	57.j	$18$	$36$	$6$	$7.282$		None		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
912.2.cc.g	$912$	$2$	912.cc	57.j	$18$	$60$	$10$	$7.282$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
912.2.cc.h	$912$	$2$	912.cc	57.j	$18$	$60$	$10$	$7.282$		None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

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