Space of modular forms of level 350 and weight 2

• Label: 350.2
• Level: 350
• Weight: 2
• Dimension: 1058
• Nonzero newspaces: 12
• Newform subspaces: 48
• Sturm bound: 14400
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 48 \)
Sturm bound:			\(14400\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(350))\).

	Total	New	Old
Modular forms	3936	1058	2878
Cusp forms	3265	1058	2207
Eisenstein series	671	0	671

Trace form

1058 * q + 2 * q^2 + 10 * q^3 + 4 * q^4 + 10 * q^5 + 14 * q^6 + 16 * q^7 + 2 * q^8 + 40 * q^9 + 10 * q^10 + 36 * q^11 + 10 * q^12 + 38 * q^13 + 14 * q^14 + 40 * q^15 + 4 * q^16 + 20 * q^17 - 12 * q^18 - 18 * q^19 + 18 * q^21 - 44 * q^22 - 8 * q^23 - 26 * q^24 - 94 * q^25 - 42 * q^26 - 140 * q^27 - 52 * q^28 - 92 * q^29 - 112 * q^30 - 84 * q^31 - 8 * q^32 - 176 * q^33 - 98 * q^34 - 52 * q^35 - 56 * q^36 - 38 * q^37 - 38 * q^38 - 144 * q^39 + 10 * q^40 - 4 * q^41 - 82 * q^42 - 36 * q^43 - 12 * q^44 - 102 * q^45 + 24 * q^46 + 4 * q^47 + 10 * q^48 + 90 * q^49 + 50 * q^50 + 84 * q^51 + 38 * q^52 + 78 * q^53 + 116 * q^54 + 16 * q^55 + 14 * q^56 - 20 * q^57 + 96 * q^58 - 42 * q^59 - 70 * q^61 - 20 * q^62 - 136 * q^63 + 4 * q^64 - 142 * q^65 + 24 * q^66 - 152 * q^67 - 60 * q^68 - 184 * q^69 - 40 * q^70 - 40 * q^71 + 38 * q^72 - 128 * q^73 - 88 * q^74 - 216 * q^75 - 18 * q^76 - 124 * q^77 - 40 * q^78 - 104 * q^79 + 10 * q^80 + 48 * q^81 - 40 * q^82 - 170 * q^83 - 2 * q^84 - 78 * q^85 - 44 * q^86 - 100 * q^87 - 12 * q^88 - 186 * q^89 - 86 * q^90 - 66 * q^91 - 64 * q^92 - 64 * q^93 - 36 * q^94 - 72 * q^95 - 34 * q^96 - 44 * q^97 - 190 * q^98 - 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(350))\)

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
350.2.a	\(\chi_{350}(1, \cdot)\)	350.2.a.a	1	1
		350.2.a.b	1
		350.2.a.c	1
		350.2.a.d	1
		350.2.a.e	1
		350.2.a.f	1
		350.2.a.g	2
		350.2.a.h	2
350.2.c	\(\chi_{350}(99, \cdot)\)	350.2.c.a	2	1
		350.2.c.b	2
		350.2.c.c	2
		350.2.c.d	2
350.2.e	\(\chi_{350}(51, \cdot)\)	350.2.e.a	2	2
		350.2.e.b	2
		350.2.e.c	2
		350.2.e.d	2
		350.2.e.e	2
		350.2.e.f	2
		350.2.e.g	2
		350.2.e.h	2
		350.2.e.i	2
		350.2.e.j	2
		350.2.e.k	2
		350.2.e.l	2
350.2.g	\(\chi_{350}(293, \cdot)\)	350.2.g.a	8	2
		350.2.g.b	16
350.2.h	\(\chi_{350}(71, \cdot)\)	350.2.h.a	8	4
		350.2.h.b	12
		350.2.h.c	16
		350.2.h.d	20
350.2.j	\(\chi_{350}(149, \cdot)\)	350.2.j.a	4	2
		350.2.j.b	4
		350.2.j.c	4
		350.2.j.d	4
		350.2.j.e	4
		350.2.j.f	4
350.2.m	\(\chi_{350}(29, \cdot)\)	350.2.m.a	24	4
		350.2.m.b	40
350.2.o	\(\chi_{350}(143, \cdot)\)	350.2.o.a	8	4
		350.2.o.b	8
		350.2.o.c	16
		350.2.o.d	16
350.2.q	\(\chi_{350}(11, \cdot)\)	350.2.q.a	8	8
		350.2.q.b	72
		350.2.q.c	80
350.2.r	\(\chi_{350}(13, \cdot)\)	350.2.r.a	160	8
350.2.u	\(\chi_{350}(9, \cdot)\)	350.2.u.a	160	8
350.2.x	\(\chi_{350}(3, \cdot)\)	350.2.x.a	320	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(350))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(350)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)