Space of modular forms of level 468, weight 2, and Character 468.c

• Label: 468.2.c
• Level: $468$
• Weight: $2$
• Character orbit: 468.c
• Rep. character: $\chi_{468}(287,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(468, [\chi])\).

	Total	New	Old
Modular forms	92	24	68
Cusp forms	76	24	52
Eisenstein series	16	0	16

Trace form

\( 24 q + 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(468, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
468.2.c.a	$468$	$2$	468.c	12.b	$2$	$4$	$4$	$3.737$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{3}q^{2}+2q^{4}-2\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\cdots\)
468.2.c.b	$468$	$2$	468.c	12.b	$2$	$8$	$8$	$3.737$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{4})q^{4}-\beta _{5}q^{5}+\cdots\)
468.2.c.c	$468$	$2$	468.c	12.b	$2$	$12$	$12$	$3.737$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{3}+\beta _{10})q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(468, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(468, [\chi]) \cong \)