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

• Label: 468.2.h
• Level: $468$
• Weight: $2$
• Character orbit: 468.h
• Rep. character: $\chi_{468}(467,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $168$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 156 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(168\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	92	28	64
Cusp forms	76	28	48
Eisenstein series	16	0	16

Trace form

\( 28 q + O(q^{10}) \)

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.h.a	$468$	$2$	468.h	156.h	$2$	$4$	$4$	$3.737$	\(\Q(\sqrt{-2}, \sqrt{13})\)	\(\Q(\sqrt{-13}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}-2q^{4}+(-1-\beta _{3})q^{7}+2\beta _{2}q^{8}+\cdots\)
468.2.h.b	$468$	$2$	468.h	156.h	$2$	$4$	$4$	$3.737$	\(\Q(\sqrt{-2}, \sqrt{13})\)	\(\Q(\sqrt{-13}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}-2q^{4}+(1+\beta _{3})q^{7}+2\beta _{2}q^{8}+\cdots\)
468.2.h.c	$468$	$2$	468.h	156.h	$2$	$4$	$4$	$3.737$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{8}^{2}q^{2}+2q^{4}-\zeta_{8}^{2}q^{5}-2\zeta_{8}^{2}q^{8}+\cdots\)
468.2.h.d	$468$	$2$	468.h	156.h	$2$	$16$	$16$	$3.737$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(-\beta _{3}-\beta _{8})q^{4}+(-\beta _{6}-\beta _{12}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(468, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)