Space of modular forms of level 138 and weight 4

• Label: 138.4
• Level: 138
• Weight: 4
• Dimension: 394
• Nonzero newspaces: 4
• Newform subspaces: 12
• Sturm bound: 4224
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(4224\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(138))\).

	Total	New	Old
Modular forms	1672	394	1278
Cusp forms	1496	394	1102
Eisenstein series	176	0	176

Trace form

394 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 - 12 * q^5 - 12 * q^6 + 32 * q^7 + 16 * q^8 - 18 * q^9 + 24 * q^10 - 24 * q^11 + 24 * q^12 - 76 * q^13 - 64 * q^14 - 712 * q^15 - 32 * q^16 - 100 * q^17 + 124 * q^18 + 400 * q^19 + 656 * q^20 + 1224 * q^21 + 1016 * q^22 + 1768 * q^23 - 48 * q^24 + 1586 * q^25 + 592 * q^26 + 186 * q^27 - 224 * q^28 - 940 * q^29 - 1568 * q^30 - 2024 * q^31 + 64 * q^32 - 1864 * q^33 - 504 * q^34 - 2668 * q^35 - 72 * q^36 - 2884 * q^37 + 80 * q^38 + 360 * q^39 + 96 * q^40 + 1016 * q^41 + 192 * q^42 + 3536 * q^43 - 96 * q^44 - 108 * q^45 + 336 * q^46 + 3976 * q^47 + 96 * q^48 + 4530 * q^49 - 356 * q^50 - 96 * q^51 - 304 * q^52 - 880 * q^53 + 3016 * q^54 - 4104 * q^55 - 256 * q^56 + 516 * q^57 + 120 * q^58 - 4708 * q^59 + 232 * q^60 + 1076 * q^61 - 352 * q^62 - 3892 * q^63 - 128 * q^64 - 456 * q^65 - 5600 * q^66 - 1768 * q^67 + 1008 * q^68 - 6976 * q^69 - 384 * q^70 - 1584 * q^71 - 2320 * q^72 - 436 * q^73 + 1016 * q^74 - 8520 * q^75 - 160 * q^76 + 384 * q^77 + 996 * q^78 - 1820 * q^79 - 192 * q^80 + 6746 * q^81 + 168 * q^82 + 1820 * q^83 + 3400 * q^84 + 3668 * q^85 - 208 * q^86 + 4866 * q^87 + 192 * q^88 + 2120 * q^89 + 216 * q^90 + 9224 * q^91 - 672 * q^92 - 528 * q^93 - 384 * q^94 - 4992 * q^95 - 192 * q^96 - 24968 * q^97 - 14252 * q^98 - 3450 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(138))\)

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
138.4.a	\(\chi_{138}(1, \cdot)\)	138.4.a.a	1	1
		138.4.a.b	1
		138.4.a.c	1
		138.4.a.d	2
		138.4.a.e	2
		138.4.a.f	3
138.4.d	\(\chi_{138}(137, \cdot)\)	138.4.d.a	24	1
138.4.e	\(\chi_{138}(13, \cdot)\)	138.4.e.a	30	10
		138.4.e.b	30
		138.4.e.c	30
		138.4.e.d	30
138.4.f	\(\chi_{138}(5, \cdot)\)	138.4.f.a	240	10

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(138))\) into lower level spaces

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