Space of modular forms of level 1620 and weight 2

• Label: 1620.2
• Level: 1620
• Weight: 2
• Dimension: 29232
• Nonzero newspaces: 24
• Sturm bound: 279936
• Trace bound: 16

Defining parameters

Level:	\( N \)	=	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(279936\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1620))\).

	Total	New	Old
Modular forms	72144	29904	42240
Cusp forms	67825	29232	38593
Eisenstein series	4319	672	3647

Trace form

29232 * q - 24 * q^2 - 40 * q^4 - 69 * q^5 - 108 * q^6 + 6 * q^7 - 30 * q^8 - 72 * q^9 - 91 * q^10 + 6 * q^11 - 36 * q^12 - 86 * q^13 - 54 * q^14 - 144 * q^16 - 84 * q^17 - 36 * q^18 - 36 * q^19 - 57 * q^20 - 270 * q^21 - 56 * q^22 - 114 * q^23 - 36 * q^24 - 147 * q^25 - 42 * q^26 - 54 * q^27 - 50 * q^28 - 174 * q^29 - 54 * q^30 - 54 * q^31 + 36 * q^32 - 126 * q^33 + 24 * q^34 - 84 * q^35 - 108 * q^36 - 188 * q^37 + 24 * q^38 - 7 * q^40 - 174 * q^41 + 54 * q^42 + 6 * q^43 + 270 * q^44 - 54 * q^45 + 2 * q^46 + 138 * q^47 + 162 * q^48 - 42 * q^49 + 159 * q^50 + 126 * q^51 + 102 * q^52 + 192 * q^53 + 216 * q^54 + 66 * q^55 + 390 * q^56 + 36 * q^57 + 118 * q^58 + 234 * q^59 + 63 * q^60 - 126 * q^61 + 366 * q^62 + 108 * q^63 + 122 * q^64 + 75 * q^65 + 36 * q^66 + 18 * q^67 + 228 * q^68 + 108 * q^69 + 41 * q^70 + 120 * q^71 - 36 * q^72 - 62 * q^73 + 114 * q^74 + 44 * q^76 + 234 * q^77 - 90 * q^78 - 42 * q^79 + 132 * q^80 - 72 * q^81 - 12 * q^82 + 174 * q^83 + 18 * q^84 - 20 * q^85 + 96 * q^86 + 288 * q^87 - 56 * q^88 + 282 * q^89 - 117 * q^90 + 126 * q^91 - 210 * q^92 + 324 * q^93 - 86 * q^94 + 252 * q^95 - 342 * q^96 + 70 * q^97 - 486 * q^98 + 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1620))\)

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
1620.2.a	\(\chi_{1620}(1, \cdot)\)	1620.2.a.a	1	1
		1620.2.a.b	1
		1620.2.a.c	1
		1620.2.a.d	1
		1620.2.a.e	1
		1620.2.a.f	1
		1620.2.a.g	2
		1620.2.a.h	2
		1620.2.a.i	3
		1620.2.a.j	3
1620.2.d	\(\chi_{1620}(649, \cdot)\)	1620.2.d.a	2	1
		1620.2.d.b	2
		1620.2.d.c	6
		1620.2.d.d	6
		1620.2.d.e	8
1620.2.e	\(\chi_{1620}(971, \cdot)\)	1620.2.e.a	48	1
		1620.2.e.b	48
1620.2.h	\(\chi_{1620}(1619, \cdot)\)	n/a	136	1
1620.2.i	\(\chi_{1620}(541, \cdot)\)	1620.2.i.a	2	2
		1620.2.i.b	2
		1620.2.i.c	2
		1620.2.i.d	2
		1620.2.i.e	2
		1620.2.i.f	2
		1620.2.i.g	2
		1620.2.i.h	2
		1620.2.i.i	2
		1620.2.i.j	2
		1620.2.i.k	2
		1620.2.i.l	2
		1620.2.i.m	4
		1620.2.i.n	4
1620.2.j	\(\chi_{1620}(1133, \cdot)\)	1620.2.j.a	24	2
		1620.2.j.b	24
1620.2.k	\(\chi_{1620}(163, \cdot)\)	n/a	272	2
1620.2.n	\(\chi_{1620}(539, \cdot)\)	n/a	280	2
1620.2.q	\(\chi_{1620}(431, \cdot)\)	n/a	192	2
1620.2.r	\(\chi_{1620}(109, \cdot)\)	1620.2.r.a	4	2
		1620.2.r.b	4
		1620.2.r.c	4
		1620.2.r.d	4
		1620.2.r.e	4
		1620.2.r.f	4
		1620.2.r.g	8
		1620.2.r.h	16
1620.2.u	\(\chi_{1620}(181, \cdot)\)	1620.2.u.a	30	6
		1620.2.u.b	42
1620.2.x	\(\chi_{1620}(53, \cdot)\)	1620.2.x.a	8	4
		1620.2.x.b	8
		1620.2.x.c	16
		1620.2.x.d	16
		1620.2.x.e	24
		1620.2.x.f	24
1620.2.y	\(\chi_{1620}(703, \cdot)\)	n/a	560	4
1620.2.bb	\(\chi_{1620}(179, \cdot)\)	n/a	624	6
1620.2.bd	\(\chi_{1620}(289, \cdot)\)	n/a	108	6
1620.2.be	\(\chi_{1620}(71, \cdot)\)	n/a	432	6
1620.2.bg	\(\chi_{1620}(61, \cdot)\)	n/a	648	18
1620.2.bi	\(\chi_{1620}(127, \cdot)\)	n/a	1248	12
1620.2.bk	\(\chi_{1620}(17, \cdot)\)	n/a	216	12
1620.2.bm	\(\chi_{1620}(59, \cdot)\)	n/a	5760	18
1620.2.bo	\(\chi_{1620}(11, \cdot)\)	n/a	3888	18
1620.2.br	\(\chi_{1620}(49, \cdot)\)	n/a	972	18
1620.2.bs	\(\chi_{1620}(77, \cdot)\)	n/a	1944	36
1620.2.bv	\(\chi_{1620}(7, \cdot)\)	n/a	11520	36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1620))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1620)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(540))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(810))\)\(^{\oplus 2}\)