Space of modular forms of level 1350 and weight 2

• Label: 1350.2
• Level: 1350
• Weight: 2
• Dimension: 11798
• Nonzero newspaces: 18
• Sturm bound: 194400
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(194400\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1350))\).

	Total	New	Old
Modular forms	50280	11798	38482
Cusp forms	46921	11798	35123
Eisenstein series	3359	0	3359

Trace form

11798 * q + q^2 + q^4 - 6 * q^6 - 4 * q^7 - 5 * q^8 - 12 * q^9 - 8 * q^10 - 50 * q^11 - 3 * q^12 - 42 * q^13 - 36 * q^14 + q^16 - 54 * q^17 + 6 * q^18 - 30 * q^19 - 8 * q^20 + 24 * q^21 - 16 * q^22 - 30 * q^23 - 16 * q^25 + 32 * q^26 + 27 * q^27 + 2 * q^28 - 12 * q^29 - 36 * q^31 + q^32 + 75 * q^33 + 58 * q^34 + 96 * q^35 + 54 * q^36 + 60 * q^37 + 227 * q^38 + 198 * q^39 + 32 * q^40 + 298 * q^41 + 168 * q^42 + 228 * q^43 + 80 * q^44 + 120 * q^45 + 96 * q^46 + 378 * q^47 + 42 * q^48 + 213 * q^49 + 160 * q^50 + 192 * q^51 + 54 * q^52 + 336 * q^53 + 108 * q^54 + 32 * q^55 + 76 * q^56 + 135 * q^57 + 46 * q^58 + 65 * q^59 + 6 * q^61 + 56 * q^62 - 6 * q^63 - 5 * q^64 + 144 * q^65 + 114 * q^67 + 57 * q^68 + 18 * q^69 + 128 * q^70 + 16 * q^71 + 24 * q^72 + 134 * q^73 + 146 * q^74 + 72 * q^75 + 39 * q^76 + 548 * q^77 + 36 * q^78 + 364 * q^79 + 192 * q^81 + 126 * q^82 + 580 * q^83 + 208 * q^85 + 34 * q^86 + 276 * q^87 + 11 * q^88 + 505 * q^89 + 206 * q^91 - 8 * q^92 + 282 * q^93 - 34 * q^94 + 136 * q^95 + 6 * q^96 + 84 * q^97 - 105 * q^98 + 204 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1350))\)

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
1350.2.a	\(\chi_{1350}(1, \cdot)\)	1350.2.a.a	1	1
		1350.2.a.b	1
		1350.2.a.c	1
		1350.2.a.d	1
		1350.2.a.e	1
		1350.2.a.f	1
		1350.2.a.g	1
		1350.2.a.h	1
		1350.2.a.i	1
		1350.2.a.j	1
		1350.2.a.k	1
		1350.2.a.l	1
		1350.2.a.m	1
		1350.2.a.n	1
		1350.2.a.o	1
		1350.2.a.p	1
		1350.2.a.q	1
		1350.2.a.r	1
		1350.2.a.s	1
		1350.2.a.t	1
		1350.2.a.u	1
		1350.2.a.v	1
		1350.2.a.w	2
		1350.2.a.x	2
1350.2.c	\(\chi_{1350}(649, \cdot)\)	1350.2.c.a	2	1
		1350.2.c.b	2
		1350.2.c.c	2
		1350.2.c.d	2
		1350.2.c.e	2
		1350.2.c.f	2
		1350.2.c.g	2
		1350.2.c.h	2
		1350.2.c.i	2
		1350.2.c.j	2
		1350.2.c.k	2
		1350.2.c.l	2
1350.2.e	\(\chi_{1350}(451, \cdot)\)	1350.2.e.a	2	2
		1350.2.e.b	2
		1350.2.e.c	2
		1350.2.e.d	2
		1350.2.e.e	2
		1350.2.e.f	2
		1350.2.e.g	2
		1350.2.e.h	2
		1350.2.e.i	2
		1350.2.e.j	4
		1350.2.e.k	4
		1350.2.e.l	4
		1350.2.e.m	4
		1350.2.e.n	4
1350.2.f	\(\chi_{1350}(107, \cdot)\)	1350.2.f.a	8	2
		1350.2.f.b	8
		1350.2.f.c	8
		1350.2.f.d	8
		1350.2.f.e	8
		1350.2.f.f	8
1350.2.h	\(\chi_{1350}(271, \cdot)\)	n/a	160	4
1350.2.j	\(\chi_{1350}(199, \cdot)\)	1350.2.j.a	4	2
		1350.2.j.b	4
		1350.2.j.c	4
		1350.2.j.d	4
		1350.2.j.e	4
		1350.2.j.f	8
		1350.2.j.g	8
1350.2.l	\(\chi_{1350}(151, \cdot)\)	n/a	342	6
1350.2.m	\(\chi_{1350}(109, \cdot)\)	n/a	160	4
1350.2.q	\(\chi_{1350}(143, \cdot)\)	1350.2.q.a	8	4
		1350.2.q.b	8
		1350.2.q.c	8
		1350.2.q.d	8
		1350.2.q.e	8
		1350.2.q.f	8
		1350.2.q.g	8
		1350.2.q.h	16
1350.2.r	\(\chi_{1350}(91, \cdot)\)	n/a	240	8
1350.2.u	\(\chi_{1350}(49, \cdot)\)	n/a	324	6
1350.2.w	\(\chi_{1350}(53, \cdot)\)	n/a	320	8
1350.2.z	\(\chi_{1350}(19, \cdot)\)	n/a	240	8
1350.2.bb	\(\chi_{1350}(257, \cdot)\)	n/a	648	12
1350.2.bc	\(\chi_{1350}(31, \cdot)\)	n/a	2160	24
1350.2.bd	\(\chi_{1350}(17, \cdot)\)	n/a	480	16
1350.2.bf	\(\chi_{1350}(79, \cdot)\)	n/a	2160	24
1350.2.bi	\(\chi_{1350}(23, \cdot)\)	n/a	4320	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1350))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1350)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 2}\)