Space of modular forms of level 290 and weight 2

• Label: 290.2
• Level: 290
• Weight: 2
• Dimension: 771
• Nonzero newspaces: 12
• Newform subspaces: 37
• Sturm bound: 10080
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 37 \)
Sturm bound:			\(10080\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(290))\).

	Total	New	Old
Modular forms	2744	771	1973
Cusp forms	2297	771	1526
Eisenstein series	447	0	447

Trace form

771 * 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 + 4 * q^12 + 14 * q^13 + 8 * q^14 + 4 * q^15 + q^16 + 18 * q^17 + 13 * q^18 + 20 * q^19 - 6 * q^20 - 80 * q^21 - 44 * q^22 - 32 * q^23 - 52 * q^24 - 55 * q^25 - 56 * q^26 - 128 * q^27 + 8 * q^28 - 83 * q^29 - 80 * q^30 - 80 * q^31 + q^32 - 120 * q^33 - 52 * q^34 - 48 * q^35 - 43 * q^36 - 18 * q^37 - 36 * q^38 - 56 * q^39 - 6 * q^40 + 42 * q^41 + 32 * q^42 + 44 * q^43 + 12 * q^44 - 22 * q^45 + 24 * q^46 - 8 * q^47 + 4 * q^48 - 55 * q^49 + q^50 - 40 * q^51 + 14 * q^52 - 72 * q^53 + 40 * q^54 - 100 * q^55 + 8 * q^56 - 32 * q^57 + 29 * q^58 + 4 * q^59 + 4 * q^60 - 50 * q^61 + 32 * q^62 - 120 * q^63 + q^64 - 49 * q^65 + 48 * q^66 - 44 * q^67 + 18 * q^68 - 16 * q^69 - 20 * q^70 - 152 * q^71 + 13 * q^72 - 108 * q^73 - 130 * q^74 - 136 * q^75 - 92 * q^76 - 184 * q^77 - 168 * q^78 - 32 * q^79 + q^80 - 327 * q^81 - 70 * q^82 - 140 * q^83 - 136 * q^84 - 150 * q^85 - 236 * q^86 - 164 * q^87 + 12 * q^88 - 190 * q^89 - 127 * q^90 - 224 * q^91 - 144 * q^92 - 96 * q^93 - 64 * q^94 - 204 * q^95 + 4 * q^96 - 28 * q^97 - 167 * q^98 - 236 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)

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
290.2.a	\(\chi_{290}(1, \cdot)\)	290.2.a.a	1	1
		290.2.a.b	2
		290.2.a.c	2
		290.2.a.d	3
		290.2.a.e	3
290.2.b	\(\chi_{290}(59, \cdot)\)	290.2.b.a	4	1
		290.2.b.b	10
290.2.c	\(\chi_{290}(231, \cdot)\)	290.2.c.a	2	1
		290.2.c.b	4
		290.2.c.c	4
290.2.d	\(\chi_{290}(289, \cdot)\)	290.2.d.a	8	1
		290.2.d.b	8
290.2.e	\(\chi_{290}(17, \cdot)\)	290.2.e.a	2	2
		290.2.e.b	2
		290.2.e.c	2
		290.2.e.d	4
		290.2.e.e	8
		290.2.e.f	12
290.2.j	\(\chi_{290}(133, \cdot)\)	290.2.j.a	2	2
		290.2.j.b	2
		290.2.j.c	2
		290.2.j.d	4
		290.2.j.e	8
		290.2.j.f	12
290.2.k	\(\chi_{290}(81, \cdot)\)	290.2.k.a	12	6
		290.2.k.b	12
		290.2.k.c	18
		290.2.k.d	18
290.2.l	\(\chi_{290}(9, \cdot)\)	290.2.l.a	48	6
		290.2.l.b	48
290.2.m	\(\chi_{290}(51, \cdot)\)	290.2.m.a	24	6
		290.2.m.b	36
290.2.n	\(\chi_{290}(49, \cdot)\)	290.2.n.a	84	6
290.2.o	\(\chi_{290}(3, \cdot)\)	290.2.o.a	84	12
		290.2.o.b	96
290.2.t	\(\chi_{290}(73, \cdot)\)	290.2.t.a	84	12
		290.2.t.b	96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(290))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(290)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 2}\)