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

• Label: 460.2.m
• Level: $460$
• Weight: $2$
• Character orbit: 460.m
• Rep. character: $\chi_{460}(41,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $80$
• 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.m (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
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	780	80	700
Cusp forms	660	80	580
Eisenstein series	120	0	120

Trace form

80 * q + 2 * q^5 - 4 * q^9 - 4 * q^13 + 22 * q^17 + 22 * q^19 + 78 * q^21 - 6 * q^23 - 8 * q^25 + 42 * q^27 + 8 * q^29 + 32 * q^31 - 20 * q^35 + 16 * q^37 - 32 * q^39 - 54 * q^41 - 68 * q^43 - 64 * q^45 + 24 * q^47 - 52 * q^49 - 116 * q^51 - 28 * q^53 - 44 * q^55 + 50 * q^57 - 4 * q^59 + 60 * q^61 + 86 * q^63 + 8 * q^65 + 52 * q^67 + 12 * q^69 - 18 * q^71 + 44 * q^73 + 82 * q^77 - 4 * q^79 + 60 * q^81 + 14 * q^83 - 2 * q^85 - 112 * q^87 - 20 * q^89 + 12 * q^91 + 4 * q^93 - 16 * q^95 - 40 * q^97 - 140 * q^99

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.m.a	$460$	$2$	460.m	23.c	$11$	$30$	$3$	$3.673$		None		✓			460.2.m.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(1\)		$\mathrm{SU}(2)[C_{11}]$
460.2.m.b	$460$	$2$	460.m	23.c	$11$	$50$	$5$	$3.673$		None		✓	✓		460.2.m.b	$2$	$0$	\(0\)	\(0\)	\(5\)	\(-1\)		$\mathrm{SU}(2)[C_{11}]$

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

\( S_{2}^{\mathrm{old}}(460, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)