Space of modular forms of level 1450 and weight 2

• Label: 1450.2
• Level: 1450
• Weight: 2
• Dimension: 19307
• Nonzero newspaces: 24
• Sturm bound: 252000
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(252000\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1450))\).

	Total	New	Old
Modular forms	64568	19307	45261
Cusp forms	61433	19307	42126
Eisenstein series	3135	0	3135

Trace form

19307 * q + 2 * q^2 + 8 * q^3 + 2 * q^4 + 10 * q^5 + 8 * q^6 + 16 * q^7 + 2 * q^8 + 26 * q^9 + 10 * q^10 + 24 * q^11 + 8 * q^12 + 28 * q^13 + 16 * q^14 + 40 * q^15 + 2 * q^16 - 4 * q^17 - 24 * q^18 - 40 * q^19 + 40 * q^21 - 28 * q^22 - 4 * q^23 - 4 * q^24 - 70 * q^25 + 23 * q^26 + 44 * q^27 - 24 * q^28 + 46 * q^29 - 40 * q^30 + 40 * q^31 - 8 * q^32 + 100 * q^33 + 21 * q^34 + 40 * q^35 + 54 * q^36 + 94 * q^37 + 68 * q^38 + 88 * q^39 + 10 * q^40 + 44 * q^41 + 64 * q^42 + 8 * q^43 + 24 * q^44 - 30 * q^45 + 48 * q^46 + 44 * q^47 + 8 * q^48 + 80 * q^49 + 50 * q^50 + 80 * q^51 + 28 * q^52 + 81 * q^53 + 80 * q^54 + 40 * q^55 + 16 * q^56 + 56 * q^57 + 30 * q^58 + 28 * q^59 + 60 * q^61 - 56 * q^62 + 40 * q^63 + 2 * q^64 - 70 * q^65 - 24 * q^66 + 32 * q^67 - 84 * q^68 - 32 * q^69 - 80 * q^70 + 96 * q^71 + 26 * q^72 + 79 * q^73 - 40 * q^74 - 120 * q^75 + 16 * q^76 + 12 * q^77 + 24 * q^78 + 56 * q^79 + 10 * q^80 + 306 * q^81 - 20 * q^82 - 40 * q^83 + 28 * q^84 - 30 * q^85 + 108 * q^86 + 120 * q^87 + 24 * q^88 + 110 * q^89 + 10 * q^90 + 232 * q^91 + 92 * q^92 + 248 * q^93 + 152 * q^94 + 120 * q^95 + 8 * q^96 + 219 * q^97 + 226 * q^98 + 388 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1450))\)

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
1450.2.a	\(\chi_{1450}(1, \cdot)\)	1450.2.a.a	1	1
		1450.2.a.b	1
		1450.2.a.c	1
		1450.2.a.d	1
		1450.2.a.e	1
		1450.2.a.f	1
		1450.2.a.g	1
		1450.2.a.h	1
		1450.2.a.i	1
		1450.2.a.j	2
		1450.2.a.k	2
		1450.2.a.l	2
		1450.2.a.m	2
		1450.2.a.n	2
		1450.2.a.o	2
		1450.2.a.p	3
		1450.2.a.q	3
		1450.2.a.r	3
		1450.2.a.s	3
		1450.2.a.t	5
		1450.2.a.u	5
1450.2.b	\(\chi_{1450}(349, \cdot)\)	1450.2.b.a	2	1
		1450.2.b.b	2
		1450.2.b.c	2
		1450.2.b.d	2
		1450.2.b.e	2
		1450.2.b.f	2
		1450.2.b.g	4
		1450.2.b.h	4
		1450.2.b.i	4
		1450.2.b.j	6
		1450.2.b.k	6
		1450.2.b.l	6
1450.2.c	\(\chi_{1450}(1101, \cdot)\)	1450.2.c.a	2	1
		1450.2.c.b	2
		1450.2.c.c	4
		1450.2.c.d	4
		1450.2.c.e	10
		1450.2.c.f	10
		1450.2.c.g	16
1450.2.d	\(\chi_{1450}(1449, \cdot)\)	1450.2.d.a	2	1
		1450.2.d.b	2
		1450.2.d.c	2
		1450.2.d.d	2
		1450.2.d.e	4
		1450.2.d.f	4
		1450.2.d.g	4
		1450.2.d.h	4
		1450.2.d.i	10
		1450.2.d.j	10
1450.2.e	\(\chi_{1450}(307, \cdot)\)	1450.2.e.a	2	2
		1450.2.e.b	2
		1450.2.e.c	2
		1450.2.e.d	4
		1450.2.e.e	8
		1450.2.e.f	10
		1450.2.e.g	10
		1450.2.e.h	12
		1450.2.e.i	20
		1450.2.e.j	20
1450.2.j	\(\chi_{1450}(157, \cdot)\)	1450.2.j.a	2	2
		1450.2.j.b	2
		1450.2.j.c	2
		1450.2.j.d	4
		1450.2.j.e	8
		1450.2.j.f	10
		1450.2.j.g	10
		1450.2.j.h	12
		1450.2.j.i	20
		1450.2.j.j	20
1450.2.k	\(\chi_{1450}(291, \cdot)\)	n/a	280	4
1450.2.l	\(\chi_{1450}(401, \cdot)\)	n/a	282	6
1450.2.m	\(\chi_{1450}(289, \cdot)\)	n/a	304	4
1450.2.n	\(\chi_{1450}(59, \cdot)\)	n/a	280	4
1450.2.o	\(\chi_{1450}(231, \cdot)\)	n/a	296	4
1450.2.p	\(\chi_{1450}(149, \cdot)\)	n/a	264	6
1450.2.q	\(\chi_{1450}(51, \cdot)\)	n/a	288	6
1450.2.r	\(\chi_{1450}(49, \cdot)\)	n/a	276	6
1450.2.s	\(\chi_{1450}(133, \cdot)\)	n/a	600	8
1450.2.x	\(\chi_{1450}(17, \cdot)\)	n/a	600	8
1450.2.y	\(\chi_{1450}(43, \cdot)\)	n/a	540	12
1450.2.bd	\(\chi_{1450}(143, \cdot)\)	n/a	540	12
1450.2.be	\(\chi_{1450}(81, \cdot)\)	n/a	1824	24
1450.2.bf	\(\chi_{1450}(71, \cdot)\)	n/a	1776	24
1450.2.bg	\(\chi_{1450}(139, \cdot)\)	n/a	1776	24
1450.2.bh	\(\chi_{1450}(9, \cdot)\)	n/a	1824	24
1450.2.bi	\(\chi_{1450}(73, \cdot)\)	n/a	3600	48
1450.2.bn	\(\chi_{1450}(3, \cdot)\)	n/a	3600	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1450))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1450)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(725))\)\(^{\oplus 2}\)