Space of modular forms of level 124 and weight 2

• Label: 124.2
• Level: 124
• Weight: 2
• Dimension: 250
• Nonzero newspaces: 8
• Newform subspaces: 13
• Sturm bound: 1920
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(1920\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(124))\).

	Total	New	Old
Modular forms	555	310	245
Cusp forms	406	250	156
Eisenstein series	149	60	89

Trace form

250 * q - 15 * q^2 - 15 * q^4 - 30 * q^5 - 15 * q^6 - 15 * q^8 - 30 * q^9 - 15 * q^10 - 15 * q^12 - 30 * q^13 - 15 * q^14 - 15 * q^16 - 30 * q^17 - 15 * q^18 - 15 * q^20 - 35 * q^21 - 15 * q^22 - 15 * q^23 - 15 * q^24 - 65 * q^25 - 15 * q^26 - 45 * q^27 - 15 * q^28 - 60 * q^29 - 30 * q^31 - 30 * q^32 - 60 * q^33 - 15 * q^34 - 30 * q^35 - 15 * q^36 - 75 * q^37 - 15 * q^38 - 35 * q^39 - 15 * q^40 - 45 * q^41 - 15 * q^42 - 5 * q^43 - 15 * q^44 - 30 * q^45 - 15 * q^46 + 30 * q^48 + 60 * q^50 + 90 * q^51 + 60 * q^52 + 150 * q^54 + 60 * q^55 + 120 * q^56 + 60 * q^57 + 90 * q^58 + 30 * q^59 + 210 * q^60 + 90 * q^61 + 75 * q^62 + 120 * q^63 + 75 * q^64 + 60 * q^65 + 210 * q^66 + 30 * q^67 + 90 * q^68 + 60 * q^69 + 120 * q^70 + 60 * q^71 + 150 * q^72 + 60 * q^74 + 75 * q^75 + 60 * q^76 - 45 * q^77 + 30 * q^78 - 35 * q^79 - 15 * q^80 - 90 * q^81 - 15 * q^82 - 105 * q^83 - 15 * q^84 - 90 * q^85 - 15 * q^86 - 60 * q^87 - 15 * q^88 - 105 * q^89 - 60 * q^90 - 65 * q^91 - 150 * q^93 - 30 * q^94 - 120 * q^95 + 30 * q^96 - 95 * q^97 - 15 * q^98 - 75 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(124))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
124.2.a	\(\chi_{124}(1, \cdot)\)	124.2.a.a	1	1
		124.2.a.b	1
124.2.d	\(\chi_{124}(123, \cdot)\)	124.2.d.a	4	1
		124.2.d.b	4
		124.2.d.c	6
124.2.e	\(\chi_{124}(5, \cdot)\)	124.2.e.a	6	2
124.2.f	\(\chi_{124}(33, \cdot)\)	124.2.f.a	4	4
		124.2.f.b	4
124.2.g	\(\chi_{124}(99, \cdot)\)	124.2.g.a	28	2
124.2.j	\(\chi_{124}(15, \cdot)\)	124.2.j.a	8	4
		124.2.j.b	48
124.2.m	\(\chi_{124}(9, \cdot)\)	124.2.m.a	24	8
124.2.p	\(\chi_{124}(3, \cdot)\)	124.2.p.a	112	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(124))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(124)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)