Space of modular forms of level 330 and weight 2

• Label: 330.2
• Level: 330
• Weight: 2
• Dimension: 645
• Nonzero newspaces: 12
• Newform subspaces: 31
• Sturm bound: 11520
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 31 \)
Sturm bound:			\(11520\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(330))\).

	Total	New	Old
Modular forms	3200	645	2555
Cusp forms	2561	645	1916
Eisenstein series	639	0	639

Trace form

645 * q + q^2 + 5 * q^3 + q^4 + 9 * q^5 + 15 * q^6 + 48 * q^7 + q^8 + 41 * q^9 + 13 * q^10 + 25 * q^11 + 9 * q^12 + 22 * q^13 + 16 * q^14 + 11 * q^15 + q^16 + 50 * q^17 - 5 * q^18 + 48 * q^19 - 7 * q^20 + 32 * q^21 - 7 * q^22 + 16 * q^23 - 5 * q^24 + 57 * q^25 + 14 * q^26 - 55 * q^27 + 8 * q^28 + 22 * q^29 - q^30 + 40 * q^31 + q^32 - 97 * q^33 - 14 * q^34 - 4 * q^35 - 9 * q^36 - 90 * q^37 - 28 * q^38 - 62 * q^39 - 23 * q^40 + 2 * q^41 - 84 * q^42 - 124 * q^43 - 47 * q^44 + 9 * q^45 - 152 * q^46 - 128 * q^47 - 11 * q^48 - 247 * q^49 - 135 * q^50 - 56 * q^51 - 98 * q^52 - 162 * q^53 - 15 * q^54 - 235 * q^55 - 8 * q^56 - 130 * q^57 - 162 * q^58 - 140 * q^59 - 47 * q^60 - 122 * q^61 - 56 * q^62 - 52 * q^63 + q^64 - 106 * q^65 + 17 * q^66 - 68 * q^67 - 30 * q^68 - 28 * q^69 + 8 * q^70 + 40 * q^71 + 57 * q^72 + 122 * q^73 + 38 * q^74 + 27 * q^75 - 4 * q^76 + 72 * q^77 + 70 * q^78 + 24 * q^79 + 29 * q^80 + 17 * q^81 - 2 * q^82 + 12 * q^83 - 8 * q^84 + 30 * q^85 + 52 * q^86 - 58 * q^87 + 33 * q^88 - 46 * q^89 - 33 * q^90 - 304 * q^91 - 24 * q^92 - 124 * q^93 - 96 * q^94 - 128 * q^95 - 11 * q^96 - 306 * q^97 - 39 * q^98 - 267 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)

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
330.2.a	\(\chi_{330}(1, \cdot)\)	330.2.a.a	1	1
		330.2.a.b	1
		330.2.a.c	1
		330.2.a.d	1
		330.2.a.e	1
330.2.c	\(\chi_{330}(199, \cdot)\)	330.2.c.a	4	1
		330.2.c.b	4
330.2.d	\(\chi_{330}(131, \cdot)\)	330.2.d.a	8	1
		330.2.d.b	8
330.2.f	\(\chi_{330}(329, \cdot)\)	330.2.f.a	24	1
330.2.j	\(\chi_{330}(23, \cdot)\)	330.2.j.a	20	2
		330.2.j.b	20
330.2.l	\(\chi_{330}(43, \cdot)\)	330.2.l.a	4	2
		330.2.l.b	4
		330.2.l.c	8
		330.2.l.d	8
330.2.m	\(\chi_{330}(31, \cdot)\)	330.2.m.a	4	4
		330.2.m.b	4
		330.2.m.c	4
		330.2.m.d	4
		330.2.m.e	8
		330.2.m.f	8
330.2.p	\(\chi_{330}(29, \cdot)\)	330.2.p.a	96	4
330.2.r	\(\chi_{330}(41, \cdot)\)	330.2.r.a	32	4
		330.2.r.b	32
330.2.s	\(\chi_{330}(49, \cdot)\)	330.2.s.a	8	4
		330.2.s.b	8
		330.2.s.c	32
330.2.u	\(\chi_{330}(7, \cdot)\)	330.2.u.a	48	8
		330.2.u.b	48
330.2.w	\(\chi_{330}(47, \cdot)\)	330.2.w.a	192	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(330))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(330)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)