Space of modular forms of level 1332 and weight 2

• Label: 1332.2
• Level: 1332
• Weight: 2
• Dimension: 22393
• Nonzero newspaces: 48
• Sturm bound: 196992
• Trace bound: 22

Defining parameters

Level:	\( N \)	=	\( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(196992\)
Trace bound:			\(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1332))\).

	Total	New	Old
Modular forms	50688	23025	27663
Cusp forms	47809	22393	25416
Eisenstein series	2879	632	2247

Trace form

22393 * q - 48 * q^2 - 44 * q^4 - 90 * q^5 - 66 * q^6 + 6 * q^7 - 54 * q^8 - 120 * q^9 - 154 * q^10 + 6 * q^11 - 84 * q^12 - 94 * q^13 - 78 * q^14 - 18 * q^15 - 68 * q^16 - 132 * q^17 - 108 * q^18 - 90 * q^20 - 138 * q^21 - 60 * q^22 - 6 * q^23 - 78 * q^24 - 90 * q^25 - 54 * q^26 - 138 * q^28 - 132 * q^29 - 36 * q^30 - 36 * q^31 + 12 * q^32 - 174 * q^33 - 28 * q^34 - 42 * q^35 - 6 * q^36 - 356 * q^37 - 54 * q^38 + 6 * q^39 - 58 * q^40 - 204 * q^41 - 36 * q^42 - 54 * q^43 - 54 * q^44 - 174 * q^45 - 186 * q^46 - 36 * q^47 - 114 * q^48 - 170 * q^49 - 96 * q^50 - 118 * q^52 - 84 * q^53 - 150 * q^54 - 36 * q^55 - 90 * q^56 - 156 * q^57 - 100 * q^58 + 30 * q^59 - 84 * q^60 - 73 * q^61 + 36 * q^62 + 6 * q^63 - 56 * q^64 + 27 * q^65 - 24 * q^66 + 54 * q^67 + 84 * q^68 - 66 * q^69 + 156 * q^70 + 120 * q^71 - 30 * q^72 - 100 * q^73 + 120 * q^74 + 24 * q^75 + 96 * q^76 + 18 * q^77 - 48 * q^78 + 102 * q^79 + 144 * q^80 - 120 * q^81 - 82 * q^82 + 18 * q^83 - 132 * q^84 - 47 * q^85 + 30 * q^86 + 18 * q^87 + 78 * q^88 - 87 * q^89 - 84 * q^90 + 66 * q^91 - 84 * q^92 - 126 * q^93 - 18 * q^94 + 192 * q^95 - 96 * q^96 + 62 * q^97 - 54 * q^98 + 162 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1332))\)

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
1332.2.a	\(\chi_{1332}(1, \cdot)\)	1332.2.a.a	1	1
		1332.2.a.b	1
		1332.2.a.c	1
		1332.2.a.d	1
		1332.2.a.e	1
		1332.2.a.f	2
		1332.2.a.g	2
		1332.2.a.h	2
		1332.2.a.i	4
1332.2.c	\(\chi_{1332}(1259, \cdot)\)	1332.2.c.a	36	1
		1332.2.c.b	36
1332.2.e	\(\chi_{1332}(73, \cdot)\)	1332.2.e.a	2	1
		1332.2.e.b	2
		1332.2.e.c	4
		1332.2.e.d	4
		1332.2.e.e	4
1332.2.g	\(\chi_{1332}(1331, \cdot)\)	1332.2.g.a	4	1
		1332.2.g.b	4
		1332.2.g.c	4
		1332.2.g.d	64
1332.2.i	\(\chi_{1332}(445, \cdot)\)	1332.2.i.a	2	2
		1332.2.i.b	2
		1332.2.i.c	34
		1332.2.i.d	34
1332.2.j	\(\chi_{1332}(433, \cdot)\)	1332.2.j.a	2	2
		1332.2.j.b	2
		1332.2.j.c	2
		1332.2.j.d	4
		1332.2.j.e	6
		1332.2.j.f	6
		1332.2.j.g	12
1332.2.k	\(\chi_{1332}(565, \cdot)\)	1332.2.k.a	2	2
		1332.2.k.b	74
1332.2.l	\(\chi_{1332}(121, \cdot)\)	1332.2.l.a	2	2
		1332.2.l.b	74
1332.2.n	\(\chi_{1332}(487, \cdot)\)	n/a	186	2
1332.2.p	\(\chi_{1332}(413, \cdot)\)	1332.2.p.a	28	2
1332.2.q	\(\chi_{1332}(529, \cdot)\)	1332.2.q.a	76	2
1332.2.s	\(\chi_{1332}(491, \cdot)\)	n/a	448	2
1332.2.u	\(\chi_{1332}(455, \cdot)\)	n/a	448	2
1332.2.z	\(\chi_{1332}(443, \cdot)\)	n/a	448	2
1332.2.bb	\(\chi_{1332}(323, \cdot)\)	n/a	152	2
1332.2.bd	\(\chi_{1332}(47, \cdot)\)	n/a	448	2
1332.2.bg	\(\chi_{1332}(517, \cdot)\)	1332.2.bg.a	4	2
		1332.2.bg.b	72
1332.2.bi	\(\chi_{1332}(397, \cdot)\)	1332.2.bi.a	2	2
		1332.2.bi.b	2
		1332.2.bi.c	2
		1332.2.bi.d	2
		1332.2.bi.e	2
		1332.2.bi.f	2
		1332.2.bi.g	4
		1332.2.bi.h	8
		1332.2.bi.i	8
1332.2.bk	\(\chi_{1332}(371, \cdot)\)	n/a	432	2
1332.2.bm	\(\chi_{1332}(359, \cdot)\)	n/a	152	2
1332.2.bn	\(\chi_{1332}(85, \cdot)\)	1332.2.bn.a	76	2
1332.2.bq	\(\chi_{1332}(11, \cdot)\)	n/a	448	2
1332.2.bs	\(\chi_{1332}(49, \cdot)\)	n/a	228	6
1332.2.bt	\(\chi_{1332}(145, \cdot)\)	1332.2.bt.a	6	6
		1332.2.bt.b	12
		1332.2.bt.c	18
		1332.2.bt.d	24
		1332.2.bt.e	36
1332.2.bu	\(\chi_{1332}(229, \cdot)\)	n/a	228	6
1332.2.bv	\(\chi_{1332}(103, \cdot)\)	n/a	896	4
1332.2.by	\(\chi_{1332}(29, \cdot)\)	n/a	152	4
1332.2.bz	\(\chi_{1332}(401, \cdot)\)	n/a	152	4
1332.2.cc	\(\chi_{1332}(125, \cdot)\)	1332.2.cc.a	56	4
1332.2.ce	\(\chi_{1332}(319, \cdot)\)	n/a	896	4
1332.2.cf	\(\chi_{1332}(31, \cdot)\)	n/a	896	4
1332.2.ci	\(\chi_{1332}(199, \cdot)\)	n/a	372	4
1332.2.cj	\(\chi_{1332}(245, \cdot)\)	n/a	152	4
1332.2.cp	\(\chi_{1332}(71, \cdot)\)	n/a	456	6
1332.2.cq	\(\chi_{1332}(155, \cdot)\)	n/a	1344	6
1332.2.cr	\(\chi_{1332}(95, \cdot)\)	n/a	1344	6
1332.2.cs	\(\chi_{1332}(215, \cdot)\)	n/a	456	6
1332.2.ct	\(\chi_{1332}(289, \cdot)\)	1332.2.ct.a	6	6
		1332.2.ct.b	6
		1332.2.ct.c	12
		1332.2.ct.d	18
		1332.2.ct.e	24
		1332.2.ct.f	24
1332.2.cu	\(\chi_{1332}(781, \cdot)\)	n/a	228	6
1332.2.dd	\(\chi_{1332}(25, \cdot)\)	n/a	228	6
1332.2.de	\(\chi_{1332}(707, \cdot)\)	n/a	1344	6
1332.2.df	\(\chi_{1332}(83, \cdot)\)	n/a	1344	6
1332.2.di	\(\chi_{1332}(79, \cdot)\)	n/a	2688	12
1332.2.dj	\(\chi_{1332}(113, \cdot)\)	n/a	456	12
1332.2.dk	\(\chi_{1332}(17, \cdot)\)	n/a	144	12
1332.2.dl	\(\chi_{1332}(19, \cdot)\)	n/a	1116	12
1332.2.dq	\(\chi_{1332}(5, \cdot)\)	n/a	456	12
1332.2.dr	\(\chi_{1332}(187, \cdot)\)	n/a	2688	12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1332))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1332)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(666))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1332))\)\(^{\oplus 1}\)