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

• Label: 124.2.e
• Level: $124$
• Weight: $2$
• Character orbit: 124.e
• Rep. character: $\chi_{124}(5,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• 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.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
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	38	6	32
Cusp forms	26	6	20
Eisenstein series	12	0	12

Trace form

6 * q + q^3 - q^5 - q^7 - 2 * q^9 - 3 * q^11 + 3 * q^13 + 6 * q^15 - 9 * q^17 + q^19 - 7 * q^21 + 16 * q^23 - 4 * q^25 - 2 * q^27 + 4 * q^29 + 14 * q^31 - 30 * q^33 - 30 * q^35 - 17 * q^37 + 2 * q^39 - 9 * q^41 - 3 * q^43 + 18 * q^45 + 8 * q^47 - 2 * q^49 + 21 * q^51 - 9 * q^53 + 21 * q^55 + 17 * q^57 + 3 * q^59 + 44 * q^61 + 32 * q^63 + q^65 - 19 * q^67 - 12 * q^69 - 5 * q^71 - 5 * q^73 + 16 * q^75 + 18 * q^77 - 29 * q^79 + 13 * q^81 - 41 * q^83 + 30 * q^85 - 24 * q^87 + 12 * q^89 - 2 * q^91 + 49 * q^93 - 82 * q^95 - 36 * q^97 - 24 * 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.e.a	$124$	$2$	124.e	31.c	$3$	$6$	$3$	$0.990$	6.0.954288.1	None		✓	✓	✓	124.2.e.a	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

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

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