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

• Label: 460.2.o
• Level: $460$
• Weight: $2$
• Character orbit: 460.o
• Rep. character: $\chi_{460}(19,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $680$
• 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.o (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 460 \)
Character field:			\(\Q(\zeta_{22})\)
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	760	760	0
Cusp forms	680	680	0
Eisenstein series	80	80	0

Trace form

680 * q - 14 * q^4 - 22 * q^5 - 6 * q^6 - 96 * q^9 - 11 * q^10 - 22 * q^14 - 14 * q^16 - 11 * q^20 - 44 * q^21 - 24 * q^24 - 18 * q^25 - 46 * q^26 - 28 * q^29 - 11 * q^30 - 44 * q^34 + 26 * q^36 - 11 * q^40 - 28 * q^41 - 154 * q^44 - 34 * q^46 + 21 * q^50 - 98 * q^54 - 22 * q^56 - 11 * q^60 - 44 * q^61 - 26 * q^64 - 22 * q^65 + 44 * q^66 - 16 * q^69 - 18 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 232 * q^81 - 22 * q^84 + 94 * q^85 + 198 * q^86 - 44 * q^89 - 242 * q^90 - 118 * q^94 + 340 * q^96

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
460.2.o.a	$460$	$2$	460.o	460.o	$22$	$40$	$4$	$3.673$		\(\Q(\sqrt{-5}) \)		✓			460.2.o.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{22}]$
460.2.o.b	$460$	$2$	460.o	460.o	$22$	$640$	$64$	$3.673$		None		✓	✓		460.2.o.b	$8$	$0$	\(0\)	\(0\)	\(-22\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$