Space of modular forms of level 124, weight 2, and Character 124.m

• Label: 124.2.m
• Level: $124$
• Weight: $2$
• Character orbit: 124.m
• Rep. character: $\chi_{124}(9,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.m (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(124, [\chi])\).

	Total	New	Old
Modular forms	152	24	128
Cusp forms	104	24	80
Eisenstein series	48	0	48

Trace form

24 * q - q^3 + q^5 - 9 * q^7 + 2 * q^9 + 8 * q^11 + 2 * q^13 - q^15 - q^17 - q^19 + 12 * q^21 - 21 * q^23 - 21 * q^25 - 43 * q^27 - 24 * q^29 - 29 * q^31 - 5 * q^33 + 10 * q^35 - 8 * q^37 - 17 * q^39 + 9 * q^41 - 2 * q^43 - 28 * q^45 - 38 * q^47 + 22 * q^49 + 69 * q^51 + 59 * q^53 - q^55 - 7 * q^57 - 13 * q^59 + 36 * q^61 + 118 * q^63 + 94 * q^65 + 29 * q^67 + 52 * q^69 + 55 * q^71 + 55 * q^73 + 79 * q^75 - 38 * q^77 - 31 * q^79 - 98 * q^81 - 59 * q^83 - 60 * q^85 - 36 * q^87 - 57 * q^89 - 48 * q^91 - 124 * q^93 - 3 * q^95 - 19 * q^97 - 31 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(124, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
124.2.m.a	$124$	$2$	124.m	31.g	$15$	$24$	$3$	$0.990$		None		✓	✓	✓	124.2.m.a	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-9\)		$\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(124, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(124, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)