Space of modular forms of level 245 and weight 2

• Label: 245.2
• Level: 245
• Weight: 2
• Dimension: 1925
• Nonzero newspaces: 12
• Newform subspaces: 46
• Sturm bound: 9408
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 46 \)
Sturm bound:			\(9408\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(245))\).

	Total	New	Old
Modular forms	2592	2215	377
Cusp forms	2113	1925	188
Eisenstein series	479	290	189

Trace form

1925 * q - 27 * q^2 - 30 * q^3 - 39 * q^4 - 50 * q^5 - 114 * q^6 - 44 * q^7 - 75 * q^8 - 57 * q^9 - 72 * q^10 - 114 * q^11 - 102 * q^12 - 60 * q^13 - 72 * q^14 - 113 * q^15 - 171 * q^16 - 72 * q^17 - 135 * q^18 - 78 * q^19 - 116 * q^20 - 158 * q^21 - 138 * q^22 - 90 * q^23 - 102 * q^24 - 66 * q^25 - 156 * q^26 - 66 * q^27 - 80 * q^28 - 72 * q^29 - 27 * q^30 - 126 * q^31 - 63 * q^32 - 42 * q^33 - 60 * q^34 - 57 * q^35 - 111 * q^36 - 4 * q^37 - 18 * q^38 + 32 * q^39 + 66 * q^40 - 72 * q^41 + 42 * q^42 - 30 * q^43 + 78 * q^44 - 5 * q^45 + 6 * q^46 - 54 * q^47 + 104 * q^48 + 40 * q^49 - 201 * q^50 - 126 * q^51 + 92 * q^52 - 96 * q^53 + 18 * q^54 - 18 * q^55 - 12 * q^56 - 90 * q^57 + 72 * q^58 - 18 * q^59 + 19 * q^60 - 22 * q^61 - 6 * q^62 - 60 * q^63 + 21 * q^64 - 49 * q^65 - 222 * q^66 - 30 * q^67 - 84 * q^68 - 90 * q^69 + 3 * q^70 - 258 * q^71 - 195 * q^72 - 48 * q^73 - 96 * q^74 - 51 * q^75 - 210 * q^76 - 126 * q^77 - 30 * q^78 - 66 * q^79 - 5 * q^80 - 129 * q^81 + 54 * q^82 - 6 * q^83 + 208 * q^84 - 87 * q^85 - 36 * q^86 + 78 * q^87 + 240 * q^88 + 267 * q^90 - 82 * q^91 + 48 * q^92 + 270 * q^93 + 120 * q^94 + 101 * q^95 + 300 * q^96 + 42 * q^97 + 408 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)

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
245.2.a	\(\chi_{245}(1, \cdot)\)	245.2.a.a	1	1
		245.2.a.b	1
		245.2.a.c	1
		245.2.a.d	2
		245.2.a.e	2
		245.2.a.f	2
		245.2.a.g	2
		245.2.a.h	2
245.2.b	\(\chi_{245}(99, \cdot)\)	245.2.b.a	2	1
		245.2.b.b	2
		245.2.b.c	2
		245.2.b.d	2
		245.2.b.e	4
		245.2.b.f	4
245.2.e	\(\chi_{245}(116, \cdot)\)	245.2.e.a	2	2
		245.2.e.b	2
		245.2.e.c	2
		245.2.e.d	2
		245.2.e.e	4
		245.2.e.f	4
		245.2.e.g	4
		245.2.e.h	4
		245.2.e.i	4
245.2.f	\(\chi_{245}(48, \cdot)\)	245.2.f.a	4	2
		245.2.f.b	4
		245.2.f.c	24
245.2.j	\(\chi_{245}(79, \cdot)\)	245.2.j.a	4	2
		245.2.j.b	4
		245.2.j.c	4
		245.2.j.d	4
		245.2.j.e	4
		245.2.j.f	4
		245.2.j.g	8
245.2.k	\(\chi_{245}(36, \cdot)\)	245.2.k.a	54	6
		245.2.k.b	66
245.2.l	\(\chi_{245}(68, \cdot)\)	245.2.l.a	4	4
		245.2.l.b	4
		245.2.l.c	8
		245.2.l.d	48
245.2.p	\(\chi_{245}(29, \cdot)\)	245.2.p.a	12	6
		245.2.p.b	144
245.2.q	\(\chi_{245}(11, \cdot)\)	245.2.q.a	96	12
		245.2.q.b	120
245.2.s	\(\chi_{245}(13, \cdot)\)	245.2.s.a	312	12
245.2.t	\(\chi_{245}(4, \cdot)\)	245.2.t.a	312	12
245.2.x	\(\chi_{245}(3, \cdot)\)	245.2.x.a	624	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(245))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(245)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 1}\)