Space of modular forms of level 930 and weight 2

• Label: 930.2
• Level: 930
• Weight: 2
• Dimension: 5265
• Nonzero newspaces: 24
• Newform subspaces: 108
• Sturm bound: 92160
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 108 \)
Sturm bound:			\(92160\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(930))\).

	Total	New	Old
Modular forms	24000	5265	18735
Cusp forms	22081	5265	16816
Eisenstein series	1919	0	1919

Trace form

5265 * q + q^2 + 5 * q^3 + q^4 + 9 * q^5 + 5 * q^6 + 8 * q^7 + q^8 + q^9 - 7 * q^10 - 20 * q^11 - 11 * q^12 - 18 * q^13 - 24 * q^14 - 19 * q^15 + q^16 - 30 * q^17 - 15 * q^18 - 12 * q^19 - 7 * q^20 + 12 * q^21 + 116 * q^22 + 96 * q^23 + 5 * q^24 + 57 * q^25 + 134 * q^26 + 5 * q^27 + 168 * q^28 + 222 * q^29 + 89 * q^30 + 225 * q^31 + q^32 + 116 * q^33 + 226 * q^34 + 96 * q^35 + 21 * q^36 + 270 * q^37 + 92 * q^38 + 98 * q^39 - 23 * q^40 + 82 * q^41 + 36 * q^42 - 44 * q^43 - 4 * q^44 + 9 * q^45 - 72 * q^46 - 48 * q^47 - 11 * q^48 + 33 * q^49 - 15 * q^50 + 174 * q^51 - 18 * q^52 + 78 * q^53 + 5 * q^54 + 100 * q^55 - 8 * q^56 + 200 * q^57 - 2 * q^58 + 100 * q^59 + 13 * q^60 + 358 * q^61 - 23 * q^62 + 248 * q^63 + q^64 + 194 * q^65 - 36 * q^66 + 92 * q^67 - 30 * q^68 + 172 * q^69 + 8 * q^70 + 120 * q^71 + 17 * q^72 + 82 * q^73 - 42 * q^74 + 17 * q^75 - 44 * q^76 + 24 * q^77 - 190 * q^78 - 96 * q^79 + 9 * q^80 - 303 * q^81 - 22 * q^82 - 108 * q^83 - 128 * q^84 - 30 * q^85 - 68 * q^86 - 298 * q^87 - 4 * q^88 - 166 * q^89 - 203 * q^90 - 144 * q^91 - 24 * q^92 - 527 * q^93 - 16 * q^94 - 28 * q^95 - 11 * q^96 - 126 * q^97 - 39 * q^98 - 304 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(930))\)

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
930.2.a	\(\chi_{930}(1, \cdot)\)	930.2.a.a	1	1
		930.2.a.b	1
		930.2.a.c	1
		930.2.a.d	1
		930.2.a.e	1
		930.2.a.f	1
		930.2.a.g	1
		930.2.a.h	1
		930.2.a.i	1
		930.2.a.j	1
		930.2.a.k	1
		930.2.a.l	1
		930.2.a.m	1
		930.2.a.n	1
		930.2.a.o	1
		930.2.a.p	2
		930.2.a.q	2
		930.2.a.r	2
930.2.d	\(\chi_{930}(559, \cdot)\)	930.2.d.a	2	1
		930.2.d.b	2
		930.2.d.c	2
		930.2.d.d	2
		930.2.d.e	2
		930.2.d.f	2
		930.2.d.g	4
		930.2.d.h	6
		930.2.d.i	6
930.2.e	\(\chi_{930}(929, \cdot)\)	930.2.e.a	32	1
		930.2.e.b	32
930.2.h	\(\chi_{930}(371, \cdot)\)	930.2.h.a	4	1
		930.2.h.b	4
		930.2.h.c	16
		930.2.h.d	16
930.2.i	\(\chi_{930}(211, \cdot)\)	930.2.i.a	2	2
		930.2.i.b	2
		930.2.i.c	2
		930.2.i.d	2
		930.2.i.e	2
		930.2.i.f	2
		930.2.i.g	2
		930.2.i.h	2
		930.2.i.i	2
		930.2.i.j	4
		930.2.i.k	4
		930.2.i.l	4
		930.2.i.m	4
		930.2.i.n	6
930.2.j	\(\chi_{930}(497, \cdot)\)	930.2.j.a	4	2
		930.2.j.b	4
		930.2.j.c	8
		930.2.j.d	8
		930.2.j.e	8
		930.2.j.f	8
		930.2.j.g	40
		930.2.j.h	40
930.2.k	\(\chi_{930}(247, \cdot)\)	930.2.k.a	32	2
		930.2.k.b	32
930.2.n	\(\chi_{930}(481, \cdot)\)	930.2.n.a	8	4
		930.2.n.b	8
		930.2.n.c	12
		930.2.n.d	12
		930.2.n.e	12
		930.2.n.f	12
		930.2.n.g	16
		930.2.n.h	16
930.2.o	\(\chi_{930}(161, \cdot)\)	930.2.o.a	4	2
		930.2.o.b	4
		930.2.o.c	4
		930.2.o.d	36
		930.2.o.e	40
930.2.r	\(\chi_{930}(119, \cdot)\)	930.2.r.a	64	2
		930.2.r.b	64
930.2.s	\(\chi_{930}(439, \cdot)\)	930.2.s.a	4	2
		930.2.s.b	8
		930.2.s.c	24
		930.2.s.d	28
930.2.v	\(\chi_{930}(401, \cdot)\)	930.2.v.a	80	4
		930.2.v.b	80
930.2.y	\(\chi_{930}(29, \cdot)\)	930.2.y.a	128	4
		930.2.y.b	128
930.2.z	\(\chi_{930}(109, \cdot)\)	930.2.z.a	8	4
		930.2.z.b	16
		930.2.z.c	32
		930.2.z.d	72
930.2.be	\(\chi_{930}(37, \cdot)\)	930.2.be.a	64	4
		930.2.be.b	64
930.2.bf	\(\chi_{930}(377, \cdot)\)	930.2.bf.a	256	4
930.2.bg	\(\chi_{930}(121, \cdot)\)	930.2.bg.a	8	8
		930.2.bg.b	16
		930.2.bg.c	16
		930.2.bg.d	16
		930.2.bg.e	16
		930.2.bg.f	16
		930.2.bg.g	24
		930.2.bg.h	24
		930.2.bg.i	24
930.2.bj	\(\chi_{930}(277, \cdot)\)	930.2.bj.a	128	8
		930.2.bj.b	128
930.2.bk	\(\chi_{930}(47, \cdot)\)	930.2.bk.a	512	8
930.2.bn	\(\chi_{930}(19, \cdot)\)	930.2.bn.a	112	8
		930.2.bn.b	144
930.2.bo	\(\chi_{930}(179, \cdot)\)	930.2.bo.a	256	8
		930.2.bo.b	256
930.2.br	\(\chi_{930}(11, \cdot)\)	930.2.br.a	176	8
		930.2.br.b	176
930.2.bs	\(\chi_{930}(107, \cdot)\)	930.2.bs.a	1024	16
930.2.bt	\(\chi_{930}(13, \cdot)\)	930.2.bt.a	256	16
		930.2.bt.b	256

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(930))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(930)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 2}\)