Space of modular forms of level 375 and weight 2

• Label: 375.2
• Level: 375
• Weight: 2
• Dimension: 3328
• Nonzero newspaces: 9
• Newform subspaces: 28
• Sturm bound: 20000
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(20000\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(375))\).

	Total	New	Old
Modular forms	5360	3584	1776
Cusp forms	4641	3328	1313
Eisenstein series	719	256	463

Trace form

3328 * q + 2 * q^2 - 30 * q^3 - 54 * q^4 - 50 * q^6 - 52 * q^7 + 18 * q^8 - 28 * q^9 - 80 * q^10 + 8 * q^11 - 22 * q^12 - 48 * q^13 + 24 * q^14 - 40 * q^15 - 142 * q^16 - 20 * q^17 - 48 * q^18 - 116 * q^19 - 70 * q^20 - 86 * q^21 - 180 * q^22 - 56 * q^23 - 158 * q^24 - 140 * q^25 - 36 * q^26 - 30 * q^27 - 244 * q^28 - 52 * q^29 - 80 * q^30 - 156 * q^31 - 82 * q^32 - 54 * q^33 - 108 * q^34 - 20 * q^35 - 112 * q^36 - 52 * q^37 - 64 * q^38 - 94 * q^39 - 180 * q^40 - 28 * q^41 - 206 * q^42 - 172 * q^43 - 192 * q^44 - 120 * q^45 - 276 * q^46 - 104 * q^47 - 218 * q^48 - 230 * q^49 - 180 * q^50 - 178 * q^51 - 400 * q^52 - 136 * q^53 - 286 * q^54 - 160 * q^55 - 120 * q^56 - 174 * q^57 - 248 * q^58 - 104 * q^59 - 100 * q^60 - 128 * q^61 - 104 * q^62 - 2 * q^63 - 46 * q^64 - 10 * q^65 + 2 * q^66 + 20 * q^67 + 124 * q^68 + 134 * q^69 - 80 * q^70 + 64 * q^71 + 268 * q^72 + 24 * q^73 + 124 * q^74 + 40 * q^75 - 140 * q^76 + 96 * q^77 + 150 * q^78 + 20 * q^79 + 28 * q^81 - 104 * q^82 - 64 * q^83 + 106 * q^84 - 230 * q^85 - 112 * q^86 - 58 * q^87 - 372 * q^88 - 216 * q^89 - 40 * q^90 - 316 * q^91 - 232 * q^92 - 218 * q^93 - 564 * q^94 - 160 * q^95 - 74 * q^96 - 520 * q^97 - 382 * q^98 - 42 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(375))\)

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
375.2.a	\(\chi_{375}(1, \cdot)\)	375.2.a.a	2	1
		375.2.a.b	2
		375.2.a.c	2
		375.2.a.d	2
		375.2.a.e	4
		375.2.a.f	4
375.2.b	\(\chi_{375}(124, \cdot)\)	375.2.b.a	4	1
		375.2.b.b	4
		375.2.b.c	8
375.2.e	\(\chi_{375}(68, \cdot)\)	375.2.e.a	16	2
		375.2.e.b	16
		375.2.e.c	32
375.2.g	\(\chi_{375}(76, \cdot)\)	375.2.g.a	4	4
		375.2.g.b	8
		375.2.g.c	12
		375.2.g.d	16
		375.2.g.e	16
375.2.i	\(\chi_{375}(49, \cdot)\)	375.2.i.a	8	4
		375.2.i.b	16
		375.2.i.c	16
		375.2.i.d	24
375.2.l	\(\chi_{375}(32, \cdot)\)	375.2.l.a	64	8
		375.2.l.b	64
		375.2.l.c	64
375.2.m	\(\chi_{375}(16, \cdot)\)	375.2.m.a	260	20
		375.2.m.b	260
375.2.o	\(\chi_{375}(4, \cdot)\)	375.2.o.a	480	20
375.2.r	\(\chi_{375}(2, \cdot)\)	375.2.r.a	1920	40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(375))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(375)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 2}\)