Space of modular forms of level 475 and weight 2

• Label: 475.2
• Level: 475
• Weight: 2
• Dimension: 7902
• Nonzero newspaces: 18
• Newform subspaces: 65
• Sturm bound: 36000
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 65 \)
Sturm bound:			\(36000\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(475))\).

	Total	New	Old
Modular forms	9504	8598	906
Cusp forms	8497	7902	595
Eisenstein series	1007	696	311

Trace form

7902 * q - 103 * q^2 - 105 * q^3 - 111 * q^4 - 134 * q^5 - 177 * q^6 - 113 * q^7 - 127 * q^8 - 123 * q^9 - 154 * q^10 - 177 * q^11 - 165 * q^12 - 137 * q^13 - 163 * q^14 - 164 * q^15 - 219 * q^16 - 122 * q^17 - 161 * q^18 - 128 * q^19 - 268 * q^20 - 198 * q^21 - 116 * q^22 - 114 * q^23 - 113 * q^24 - 114 * q^25 - 375 * q^26 - 138 * q^27 - 128 * q^28 - 135 * q^29 - 164 * q^30 - 195 * q^31 - 198 * q^32 - 207 * q^33 - 200 * q^34 - 184 * q^35 - 331 * q^36 - 190 * q^37 - 200 * q^38 - 300 * q^39 - 174 * q^40 - 215 * q^41 - 179 * q^42 - 144 * q^43 - 197 * q^44 - 94 * q^45 - 258 * q^46 - 158 * q^47 - 171 * q^48 - 140 * q^49 - 94 * q^50 - 391 * q^51 - 139 * q^52 - 151 * q^53 - 158 * q^54 - 164 * q^55 - 326 * q^56 - 152 * q^57 - 290 * q^58 - 162 * q^59 - 124 * q^60 - 263 * q^61 - 168 * q^62 - 209 * q^63 - 269 * q^64 - 154 * q^65 - 369 * q^66 - 246 * q^67 - 235 * q^68 - 248 * q^69 - 204 * q^70 - 280 * q^71 - 57 * q^72 - 249 * q^73 - 195 * q^74 - 164 * q^75 - 459 * q^76 - 273 * q^77 - 29 * q^78 - 135 * q^79 + 62 * q^80 - 72 * q^81 + 8 * q^82 + 108 * q^83 + 503 * q^84 + 70 * q^85 + 12 * q^86 + 355 * q^87 + 501 * q^88 + 108 * q^89 + 266 * q^90 + 27 * q^91 + 306 * q^92 + 381 * q^93 + 466 * q^94 - 46 * q^95 + 530 * q^96 + 140 * q^97 + 286 * q^98 + 292 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(475))\)

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
475.2.a	\(\chi_{475}(1, \cdot)\)	475.2.a.a	1	1
		475.2.a.b	1
		475.2.a.c	1
		475.2.a.d	3
		475.2.a.e	3
		475.2.a.f	3
		475.2.a.g	3
		475.2.a.h	3
		475.2.a.i	4
		475.2.a.j	6
475.2.b	\(\chi_{475}(324, \cdot)\)	475.2.b.a	2	1
		475.2.b.b	6
		475.2.b.c	6
		475.2.b.d	6
		475.2.b.e	8
475.2.e	\(\chi_{475}(26, \cdot)\)	475.2.e.a	2	2
		475.2.e.b	2
		475.2.e.c	2
		475.2.e.d	6
		475.2.e.e	8
		475.2.e.f	12
		475.2.e.g	12
		475.2.e.h	12
475.2.g	\(\chi_{475}(18, \cdot)\)	475.2.g.a	4	2
		475.2.g.b	12
		475.2.g.c	16
		475.2.g.d	24
475.2.h	\(\chi_{475}(96, \cdot)\)	475.2.h.a	84	4
		475.2.h.b	100
475.2.j	\(\chi_{475}(49, \cdot)\)	475.2.j.a	4	2
		475.2.j.b	12
		475.2.j.c	16
		475.2.j.d	24
475.2.l	\(\chi_{475}(101, \cdot)\)	475.2.l.a	6	6
		475.2.l.b	18
		475.2.l.c	18
		475.2.l.d	42
		475.2.l.e	42
		475.2.l.f	48
475.2.n	\(\chi_{475}(39, \cdot)\)	475.2.n.a	80	4
		475.2.n.b	96
475.2.p	\(\chi_{475}(107, \cdot)\)	475.2.p.a	4	4
		475.2.p.b	4
		475.2.p.c	4
		475.2.p.d	4
		475.2.p.e	16
		475.2.p.f	16
		475.2.p.g	16
		475.2.p.h	24
		475.2.p.i	24
475.2.r	\(\chi_{475}(11, \cdot)\)	475.2.r.a	384	8
475.2.u	\(\chi_{475}(24, \cdot)\)	475.2.u.a	12	6
		475.2.u.b	36
		475.2.u.c	36
		475.2.u.d	84
475.2.v	\(\chi_{475}(37, \cdot)\)	475.2.v.a	16	8
		475.2.v.b	368
475.2.x	\(\chi_{475}(64, \cdot)\)	475.2.x.a	384	8
475.2.bb	\(\chi_{475}(32, \cdot)\)	475.2.bb.a	72	12
		475.2.bb.b	96
		475.2.bb.c	168
475.2.bc	\(\chi_{475}(6, \cdot)\)	475.2.bc.a	1152	24
475.2.be	\(\chi_{475}(8, \cdot)\)	475.2.be.a	768	16
475.2.bg	\(\chi_{475}(4, \cdot)\)	475.2.bg.a	1152	24
475.2.bi	\(\chi_{475}(2, \cdot)\)	475.2.bi.a	2304	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(475))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(475)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)