Space of modular forms of level 315 and weight 3

• Label: 315.3
• Level: 315
• Weight: 3
• Dimension: 4670
• Nonzero newspaces: 30
• Newform subspaces: 50
• Sturm bound: 20736
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 30 \)
Newform subspaces:			\( 50 \)
Sturm bound:			\(20736\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(315))\).

	Total	New	Old
Modular forms	7296	4938	2358
Cusp forms	6528	4670	1858
Eisenstein series	768	268	500

Trace form

4670 * q - 22 * q^2 - 20 * q^3 - 30 * q^4 - 10 * q^5 - 4 * q^6 - 10 * q^7 + 30 * q^8 - 4 * q^9 + 52 * q^10 + 52 * q^11 + 128 * q^12 + 88 * q^13 + 246 * q^14 - 20 * q^15 + 214 * q^16 + 56 * q^17 - 8 * q^18 - 44 * q^19 - 150 * q^20 - 96 * q^21 - 64 * q^22 - 220 * q^23 - 324 * q^24 + 176 * q^25 + 52 * q^26 + 52 * q^27 - 222 * q^28 + 84 * q^29 - 34 * q^30 + 164 * q^31 + 170 * q^32 + 44 * q^33 + 416 * q^34 - 26 * q^35 - 764 * q^36 - 124 * q^37 - 852 * q^38 - 680 * q^39 - 738 * q^40 - 752 * q^41 - 384 * q^42 - 288 * q^43 - 1332 * q^44 - 40 * q^45 - 876 * q^46 - 484 * q^47 - 364 * q^48 - 38 * q^49 + 782 * q^50 - 268 * q^51 + 144 * q^52 - 376 * q^53 - 736 * q^54 + 76 * q^55 - 546 * q^56 + 172 * q^57 + 916 * q^58 + 1008 * q^59 + 590 * q^60 + 976 * q^61 + 1096 * q^62 + 252 * q^63 + 118 * q^64 + 308 * q^65 + 964 * q^66 + 12 * q^67 + 1840 * q^68 + 1320 * q^69 + 150 * q^70 + 1252 * q^71 + 2544 * q^72 + 316 * q^73 + 888 * q^74 - 812 * q^75 - 216 * q^76 + 632 * q^77 - 376 * q^78 + 96 * q^79 - 3094 * q^80 - 1612 * q^81 - 1388 * q^82 - 2488 * q^83 - 1836 * q^84 - 1472 * q^85 - 5228 * q^86 - 2492 * q^87 - 3864 * q^88 - 2940 * q^89 - 2294 * q^90 - 2776 * q^91 - 2884 * q^92 - 444 * q^93 - 3328 * q^94 - 1314 * q^95 - 1184 * q^96 - 2748 * q^97 - 3258 * q^98 + 520 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(315))\)

We only show spaces with odd 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
315.3.c	\(\chi_{315}(71, \cdot)\)	315.3.c.a	16	1
315.3.e	\(\chi_{315}(244, \cdot)\)	315.3.e.a	1	1
		315.3.e.b	1
		315.3.e.c	4
		315.3.e.d	16
		315.3.e.e	16
315.3.f	\(\chi_{315}(134, \cdot)\)	315.3.f.a	24	1
315.3.h	\(\chi_{315}(181, \cdot)\)	315.3.h.a	2	1
		315.3.h.b	2
		315.3.h.c	12
		315.3.h.d	12
315.3.n	\(\chi_{315}(62, \cdot)\)	315.3.n.a	64	2
315.3.o	\(\chi_{315}(127, \cdot)\)	315.3.o.a	12	2
		315.3.o.b	24
		315.3.o.c	24
315.3.q	\(\chi_{315}(229, \cdot)\)	315.3.q.a	184	2
315.3.s	\(\chi_{315}(11, \cdot)\)	315.3.s.a	128	2
315.3.v	\(\chi_{315}(254, \cdot)\)	315.3.v.a	184	2
315.3.w	\(\chi_{315}(136, \cdot)\)	315.3.w.a	8	2
		315.3.w.b	12
		315.3.w.c	12
		315.3.w.d	20
315.3.x	\(\chi_{315}(76, \cdot)\)	315.3.x.a	128	2
315.3.y	\(\chi_{315}(44, \cdot)\)	315.3.y.a	64	2
315.3.ba	\(\chi_{315}(29, \cdot)\)	315.3.ba.a	144	2
315.3.bc	\(\chi_{315}(31, \cdot)\)	315.3.bc.a	128	2
315.3.bd	\(\chi_{315}(191, \cdot)\)	315.3.bd.a	128	2
315.3.bg	\(\chi_{315}(34, \cdot)\)	315.3.bg.a	4	2
		315.3.bg.b	4
		315.3.bg.c	176
315.3.bi	\(\chi_{315}(19, \cdot)\)	315.3.bi.a	4	2
		315.3.bi.b	4
		315.3.bi.c	12
		315.3.bi.d	24
		315.3.bi.e	32
315.3.bk	\(\chi_{315}(176, \cdot)\)	315.3.bk.a	96	2
315.3.bm	\(\chi_{315}(116, \cdot)\)	315.3.bm.a	40	2
315.3.bn	\(\chi_{315}(94, \cdot)\)	315.3.bn.a	184	2
315.3.bp	\(\chi_{315}(166, \cdot)\)	315.3.bp.a	128	2
315.3.br	\(\chi_{315}(74, \cdot)\)	315.3.br.a	184	2
315.3.bt	\(\chi_{315}(58, \cdot)\)	315.3.bt.a	368	4
315.3.bu	\(\chi_{315}(38, \cdot)\)	315.3.bu.a	368	4
315.3.bw	\(\chi_{315}(47, \cdot)\)	315.3.bw.a	368	4
315.3.by	\(\chi_{315}(22, \cdot)\)	315.3.by.a	288	4
315.3.ca	\(\chi_{315}(37, \cdot)\)	315.3.ca.a	24	4
		315.3.ca.b	64
		315.3.ca.c	64
315.3.cd	\(\chi_{315}(17, \cdot)\)	315.3.cd.a	128	4
315.3.cf	\(\chi_{315}(83, \cdot)\)	315.3.cf.a	368	4
315.3.ch	\(\chi_{315}(67, \cdot)\)	315.3.ch.a	368	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(315))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(315)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)