Space of modular forms of level 950 and weight 2

• Label: 950.2
• Level: 950
• Weight: 2
• Dimension: 8247
• Nonzero newspaces: 18
• Newform subspaces: 99
• Sturm bound: 108000
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 99 \)
Sturm bound:			\(108000\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(950))\).

	Total	New	Old
Modular forms	28008	8247	19761
Cusp forms	25993	8247	17746
Eisenstein series	2015	0	2015

Trace form

8247 * q + 2 * q^2 + 8 * q^3 + 2 * q^4 + 10 * q^5 + 8 * q^6 + 16 * q^7 + 2 * q^8 + 26 * q^9 + 10 * q^10 + 24 * q^11 + 14 * q^12 + 52 * q^13 + 34 * q^14 + 40 * q^15 + 2 * q^16 + 14 * q^17 + 3 * q^18 + 22 * q^19 + 26 * q^21 - 29 * q^22 - 14 * q^23 - 32 * q^24 - 70 * q^25 + 6 * q^26 - 7 * q^27 - 18 * q^28 - 2 * q^29 - 40 * q^30 + 2 * q^31 - 8 * q^32 + 70 * q^33 - 14 * q^34 + 40 * q^35 + 26 * q^36 + 84 * q^37 + 20 * q^38 + 86 * q^39 + 10 * q^40 + 62 * q^41 + 64 * q^42 + 50 * q^43 + 33 * q^44 - 30 * q^45 + 84 * q^46 + 88 * q^47 + 17 * q^48 + 84 * q^49 + 50 * q^50 + 123 * q^51 + 34 * q^52 + 90 * q^53 + 134 * q^54 + 40 * q^55 + 52 * q^56 + 90 * q^57 + 96 * q^58 + 90 * q^59 + 82 * q^61 - 2 * q^62 + 24 * q^63 + 8 * q^64 - 70 * q^65 + 48 * q^66 + 54 * q^67 - 75 * q^68 - 34 * q^69 - 80 * q^70 + 56 * q^71 + 35 * q^72 + 21 * q^73 - 124 * q^74 - 120 * q^75 - 20 * q^76 - 236 * q^77 - 340 * q^78 - 210 * q^79 + 10 * q^80 - 395 * q^81 - 328 * q^82 - 512 * q^83 - 434 * q^84 - 318 * q^85 - 284 * q^86 - 1012 * q^87 + 24 * q^88 - 390 * q^89 - 350 * q^90 - 416 * q^91 - 244 * q^92 - 866 * q^93 - 408 * q^94 - 156 * q^95 + 8 * q^96 - 186 * q^97 - 390 * q^98 - 753 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(950))\)

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
950.2.a	\(\chi_{950}(1, \cdot)\)	950.2.a.a	1	1
		950.2.a.b	1
		950.2.a.c	1
		950.2.a.d	1
		950.2.a.e	1
		950.2.a.f	2
		950.2.a.g	2
		950.2.a.h	2
		950.2.a.i	3
		950.2.a.j	3
		950.2.a.k	3
		950.2.a.l	3
		950.2.a.m	3
		950.2.a.n	3
950.2.b	\(\chi_{950}(799, \cdot)\)	950.2.b.a	2	1
		950.2.b.b	2
		950.2.b.c	2
		950.2.b.d	2
		950.2.b.e	2
		950.2.b.f	4
		950.2.b.g	6
		950.2.b.h	6
950.2.e	\(\chi_{950}(201, \cdot)\)	950.2.e.a	2	2
		950.2.e.b	2
		950.2.e.c	2
		950.2.e.d	2
		950.2.e.e	2
		950.2.e.f	2
		950.2.e.g	2
		950.2.e.h	4
		950.2.e.i	4
		950.2.e.j	4
		950.2.e.k	4
		950.2.e.l	8
		950.2.e.m	8
		950.2.e.n	10
		950.2.e.o	10
950.2.f	\(\chi_{950}(493, \cdot)\)	950.2.f.a	4	2
		950.2.f.b	8
		950.2.f.c	16
		950.2.f.d	32
950.2.h	\(\chi_{950}(191, \cdot)\)	950.2.h.a	4	4
		950.2.h.b	40
		950.2.h.c	44
		950.2.h.d	44
		950.2.h.e	44
950.2.j	\(\chi_{950}(49, \cdot)\)	950.2.j.a	4	2
		950.2.j.b	4
		950.2.j.c	4
		950.2.j.d	4
		950.2.j.e	4
		950.2.j.f	8
		950.2.j.g	8
		950.2.j.h	8
		950.2.j.i	16
950.2.l	\(\chi_{950}(101, \cdot)\)	950.2.l.a	6	6
		950.2.l.b	6
		950.2.l.c	6
		950.2.l.d	6
		950.2.l.e	6
		950.2.l.f	6
		950.2.l.g	12
		950.2.l.h	12
		950.2.l.i	18
		950.2.l.j	24
		950.2.l.k	24
		950.2.l.l	30
		950.2.l.m	30
950.2.n	\(\chi_{950}(39, \cdot)\)	950.2.n.a	88	4
		950.2.n.b	96
950.2.q	\(\chi_{950}(107, \cdot)\)	950.2.q.a	8	4
		950.2.q.b	8
		950.2.q.c	8
		950.2.q.d	8
		950.2.q.e	24
		950.2.q.f	32
		950.2.q.g	32
950.2.r	\(\chi_{950}(11, \cdot)\)	950.2.r.a	200	8
		950.2.r.b	200
950.2.u	\(\chi_{950}(99, \cdot)\)	950.2.u.a	12	6
		950.2.u.b	12
		950.2.u.c	12
		950.2.u.d	12
		950.2.u.e	24
		950.2.u.f	24
		950.2.u.g	36
		950.2.u.h	48
950.2.w	\(\chi_{950}(37, \cdot)\)	950.2.w.a	400	8
950.2.x	\(\chi_{950}(159, \cdot)\)	950.2.x.a	400	8
950.2.bb	\(\chi_{950}(143, \cdot)\)	950.2.bb.a	24	12
		950.2.bb.b	48
		950.2.bb.c	72
		950.2.bb.d	96
		950.2.bb.e	120
950.2.bc	\(\chi_{950}(61, \cdot)\)	950.2.bc.a	600	24
		950.2.bc.b	600
950.2.bd	\(\chi_{950}(27, \cdot)\)	950.2.bd.a	800	16
950.2.bg	\(\chi_{950}(9, \cdot)\)	950.2.bg.a	1200	24
950.2.bi	\(\chi_{950}(3, \cdot)\)	950.2.bi.a	2400	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(950))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(950)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)\(^{\oplus 2}\)