Space of modular forms of level 460, weight 2, and Character 460.i

• Label: 460.2.i
• Level: $460$
• Weight: $2$
• Character orbit: 460.i
• Rep. character: $\chi_{460}(137,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(460, [\chi])\).

	Total	New	Old
Modular forms	156	24	132
Cusp forms	132	24	108
Eisenstein series	24	0	24

Trace form

\( 24 q - 4 q^{3} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(460, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
460.2.i.a	$460$	$2$	460.i	115.e	$4$	$8$	$4$	$3.673$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{3})q^{3}+(-\beta _{1}+\beta _{6})q^{5}-\beta _{2}q^{7}+\cdots\)
460.2.i.b	$460$	$2$	460.i	115.e	$4$	$16$	$8$	$3.673$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{15})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(460, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(460, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)