Space of modular forms of level 138 and weight 2

• Label: 138.2
• Level: 138
• Weight: 2
• Dimension: 133
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 2112
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(2112\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(138))\).

	Total	New	Old
Modular forms	616	133	483
Cusp forms	441	133	308
Eisenstein series	175	0	175

Trace form

133 * q + q^2 + q^3 + q^4 + 6 * q^5 + q^6 + 8 * q^7 + q^8 + q^9 + 6 * q^10 + 12 * q^11 + q^12 + 14 * q^13 + 8 * q^14 - 16 * q^15 + q^16 - 26 * q^17 - 43 * q^18 - 24 * q^19 - 38 * q^20 - 58 * q^21 - 32 * q^22 - 65 * q^23 + q^24 - 57 * q^25 - 30 * q^26 - 65 * q^27 - 36 * q^28 - 14 * q^29 - 38 * q^30 - 12 * q^31 + q^32 - 10 * q^33 + 18 * q^34 + 4 * q^35 + q^36 - 50 * q^37 + 20 * q^38 - 30 * q^39 + 6 * q^40 - 2 * q^41 + 8 * q^42 - 44 * q^43 + 12 * q^44 + 6 * q^45 + 23 * q^46 - 40 * q^47 + q^48 - 75 * q^49 + 31 * q^50 - 26 * q^51 + 14 * q^52 + 10 * q^53 + 23 * q^54 - 16 * q^55 + 8 * q^56 + 42 * q^57 + 30 * q^58 + 16 * q^59 + 28 * q^60 + 62 * q^61 + 32 * q^62 + 118 * q^63 + q^64 + 84 * q^65 + 100 * q^66 + 68 * q^67 + 18 * q^68 + 133 * q^69 + 48 * q^70 + 72 * q^71 + 45 * q^72 + 74 * q^73 + 38 * q^74 + 163 * q^75 + 20 * q^76 + 96 * q^77 + 80 * q^78 + 36 * q^79 + 6 * q^80 + 45 * q^81 + 42 * q^82 + 40 * q^83 + 30 * q^84 + 64 * q^85 + 44 * q^86 - 36 * q^87 + 12 * q^88 + 46 * q^89 + 6 * q^90 + 24 * q^91 + 23 * q^92 + 32 * q^93 + 48 * q^94 - 12 * q^95 + q^96 - 78 * q^97 - 31 * q^98 - 98 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)

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
138.2.a	\(\chi_{138}(1, \cdot)\)	138.2.a.a	1	1
		138.2.a.b	1
		138.2.a.c	1
		138.2.a.d	2
138.2.d	\(\chi_{138}(137, \cdot)\)	138.2.d.a	8	1
138.2.e	\(\chi_{138}(13, \cdot)\)	138.2.e.a	10	10
		138.2.e.b	10
		138.2.e.c	10
		138.2.e.d	10
138.2.f	\(\chi_{138}(5, \cdot)\)	138.2.f.a	80	10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(138))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(138)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)