Space of modular forms of level 575 and weight 2

• Label: 575.2
• Level: 575
• Weight: 2
• Dimension: 11691
• Nonzero newspaces: 12
• Newform subspaces: 46
• Sturm bound: 52800
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 46 \)
Sturm bound:			\(52800\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(575))\).

	Total	New	Old
Modular forms	13816	12551	1265
Cusp forms	12585	11691	894
Eisenstein series	1231	860	371

Trace form

11691 * q - 129 * q^2 - 131 * q^3 - 137 * q^4 - 166 * q^5 - 219 * q^6 - 139 * q^7 - 153 * q^8 - 149 * q^9 - 186 * q^10 - 219 * q^11 - 179 * q^12 - 151 * q^13 - 171 * q^14 - 196 * q^15 - 247 * q^16 - 150 * q^17 - 195 * q^18 - 134 * q^19 - 156 * q^20 - 252 * q^21 - 148 * q^22 - 159 * q^23 - 312 * q^24 - 146 * q^25 - 461 * q^26 - 176 * q^27 - 159 * q^28 - 154 * q^29 - 196 * q^30 - 230 * q^31 - 201 * q^32 - 190 * q^33 - 203 * q^34 - 216 * q^35 - 320 * q^36 - 233 * q^37 - 238 * q^38 - 199 * q^39 - 206 * q^40 - 261 * q^41 - 225 * q^42 - 175 * q^43 - 250 * q^44 - 126 * q^45 - 313 * q^46 - 326 * q^47 - 181 * q^48 - 193 * q^49 - 126 * q^50 - 463 * q^51 - 209 * q^52 - 163 * q^53 - 213 * q^54 - 196 * q^55 - 372 * q^56 - 200 * q^57 - 262 * q^58 - 209 * q^59 - 156 * q^60 - 283 * q^61 - 161 * q^62 - 206 * q^63 - 245 * q^64 - 186 * q^65 - 388 * q^66 - 201 * q^67 - 278 * q^68 - 214 * q^69 - 412 * q^70 - 314 * q^71 - 338 * q^72 - 213 * q^73 - 230 * q^74 - 196 * q^75 - 594 * q^76 - 254 * q^77 - 375 * q^78 - 291 * q^79 - 186 * q^80 - 461 * q^81 - 245 * q^82 - 148 * q^83 - 391 * q^84 - 106 * q^85 - 351 * q^86 - 235 * q^87 + 137 * q^88 - 119 * q^89 - 126 * q^90 - 318 * q^91 - 260 * q^92 - 394 * q^93 - 212 * q^94 - 152 * q^95 - 204 * q^96 + 126 * q^97 + 75 * q^98 + 78 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)

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
575.2.a	\(\chi_{575}(1, \cdot)\)	575.2.a.a	1	1
		575.2.a.b	1
		575.2.a.c	1
		575.2.a.d	1
		575.2.a.e	1
		575.2.a.f	2
		575.2.a.g	2
		575.2.a.h	4
		575.2.a.i	4
		575.2.a.j	4
		575.2.a.k	7
		575.2.a.l	7
575.2.b	\(\chi_{575}(24, \cdot)\)	575.2.b.a	2	1
		575.2.b.b	2
		575.2.b.c	4
		575.2.b.d	4
		575.2.b.e	8
		575.2.b.f	14
575.2.e	\(\chi_{575}(68, \cdot)\)	575.2.e.a	4	2
		575.2.e.b	8
		575.2.e.c	12
		575.2.e.d	20
		575.2.e.e	24
575.2.g	\(\chi_{575}(116, \cdot)\)	575.2.g.a	4	4
		575.2.g.b	108
		575.2.g.c	112
575.2.i	\(\chi_{575}(139, \cdot)\)	575.2.i.a	216	4
575.2.k	\(\chi_{575}(26, \cdot)\)	575.2.k.a	10	10
		575.2.k.b	10
		575.2.k.c	20
		575.2.k.d	50
		575.2.k.e	80
		575.2.k.f	80
		575.2.k.g	100
575.2.m	\(\chi_{575}(22, \cdot)\)	575.2.m.a	464	8
575.2.p	\(\chi_{575}(49, \cdot)\)	575.2.p.a	20	10
		575.2.p.b	20
		575.2.p.c	40
		575.2.p.d	100
		575.2.p.e	160
575.2.r	\(\chi_{575}(7, \cdot)\)	575.2.r.a	160	20
		575.2.r.b	200
		575.2.r.c	320
575.2.s	\(\chi_{575}(6, \cdot)\)	575.2.s.a	2320	40
575.2.u	\(\chi_{575}(4, \cdot)\)	575.2.u.a	2320	40
575.2.w	\(\chi_{575}(17, \cdot)\)	575.2.w.a	4640	80

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(575))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(575)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)