Space of modular forms of level 190 and weight 2

• Label: 190.2
• Level: 190
• Weight: 2
• Dimension: 331
• Nonzero newspaces: 9
• Newform subspaces: 20
• Sturm bound: 4320
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 20 \)
Sturm bound:			\(4320\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(190))\).

	Total	New	Old
Modular forms	1224	331	893
Cusp forms	937	331	606
Eisenstein series	287	0	287

Trace form

331 * q + q^2 + 4 * q^3 + q^4 + q^5 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 + q^10 + 12 * q^11 - 8 * q^12 - 34 * q^13 - 28 * q^14 - 32 * q^15 + q^16 - 18 * q^17 - 41 * q^18 - 65 * q^19 - 17 * q^20 - 52 * q^21 - 42 * q^22 - 12 * q^23 + 4 * q^24 - 35 * q^25 - 22 * q^26 - 26 * q^27 - 4 * q^28 - 6 * q^29 + 4 * q^30 - 4 * q^31 + q^32 - 60 * q^33 + 18 * q^34 - 28 * q^35 + 13 * q^36 + 2 * q^37 + 19 * q^38 - 52 * q^39 + q^40 + 6 * q^41 + 32 * q^42 - 40 * q^43 - 6 * q^44 - 95 * q^45 - 48 * q^46 - 96 * q^47 - 14 * q^48 - 63 * q^49 - 71 * q^50 - 126 * q^51 + 2 * q^52 - 90 * q^53 - 68 * q^54 - 60 * q^55 - 64 * q^56 - 104 * q^57 - 42 * q^58 - 120 * q^59 - 32 * q^60 - 94 * q^61 - 76 * q^62 - 88 * q^63 - 11 * q^64 - 94 * q^65 - 96 * q^66 - 88 * q^67 - 12 * q^69 - 28 * q^70 - 72 * q^71 - 5 * q^72 + 8 * q^73 + 38 * q^74 - 8 * q^75 + 19 * q^76 + 96 * q^77 + 128 * q^78 + 68 * q^79 + q^80 + 211 * q^81 + 114 * q^82 + 156 * q^83 + 140 * q^84 + 234 * q^85 + 116 * q^86 + 336 * q^87 + 12 * q^88 + 162 * q^89 + 283 * q^90 + 208 * q^91 + 96 * q^92 + 404 * q^93 + 192 * q^94 + 145 * q^95 + 4 * q^96 + 134 * q^97 + 201 * q^98 + 318 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)

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
190.2.a	\(\chi_{190}(1, \cdot)\)	190.2.a.a	1	1
		190.2.a.b	1
		190.2.a.c	1
		190.2.a.d	2
190.2.b	\(\chi_{190}(39, \cdot)\)	190.2.b.a	4	1
		190.2.b.b	6
190.2.e	\(\chi_{190}(11, \cdot)\)	190.2.e.a	2	2
		190.2.e.b	2
		190.2.e.c	4
190.2.f	\(\chi_{190}(37, \cdot)\)	190.2.f.a	4	2
		190.2.f.b	16
190.2.i	\(\chi_{190}(49, \cdot)\)	190.2.i.a	20	2
190.2.k	\(\chi_{190}(61, \cdot)\)	190.2.k.a	6	6
		190.2.k.b	12
		190.2.k.c	12
		190.2.k.d	18
190.2.m	\(\chi_{190}(27, \cdot)\)	190.2.m.a	8	4
		190.2.m.b	32
190.2.p	\(\chi_{190}(9, \cdot)\)	190.2.p.a	60	6
190.2.r	\(\chi_{190}(3, \cdot)\)	190.2.r.a	120	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(190))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(190)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)