Space of modular forms of level 52, weight 2, and Character 52.h

• Label: 52.2.h
• Level: $52$
• Weight: $2$
• Character orbit: 52.h
• Rep. character: $\chi_{52}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $14$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	52.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(14\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(52, [\chi])\).

	Total	New	Old
Modular forms	20	2	18
Cusp forms	8	2	6
Eisenstein series	12	0	12

Trace form

\( 2 q + q^{3} - 3 q^{7} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(52, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
52.2.h.a	$52$	$2$	52.h	13.e	$6$	$2$	$1$	$0.415$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(52, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(52, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)