Space of modular forms of level 3450 and weight 2

• Label: 3450.2
• Level: 3450
• Weight: 2
• Dimension: 72722
• Nonzero newspaces: 24
• Sturm bound: 1267200
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(1267200\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3450))\).

	Total	New	Old
Modular forms	321728	72722	249006
Cusp forms	311873	72722	239151
Eisenstein series	9855	0	9855

Trace form

72722 * q - 6 * q^2 - 14 * q^3 - 6 * q^4 - 20 * q^5 - 14 * q^6 - 48 * q^7 - 6 * q^8 - 6 * q^9 - 4 * q^10 - 8 * q^11 + 18 * q^12 - 20 * q^13 + 16 * q^14 + 8 * q^15 - 6 * q^16 + 24 * q^17 + 2 * q^18 + 60 * q^19 + 16 * q^20 - 2 * q^21 + 76 * q^22 - 32 * q^23 + 26 * q^24 + 172 * q^25 - 48 * q^26 - 80 * q^27 - 12 * q^28 + 32 * q^29 + 40 * q^30 - 12 * q^31 + 14 * q^32 + 18 * q^33 + 56 * q^34 + 16 * q^35 - 6 * q^36 - 40 * q^37 - 24 * q^38 + 64 * q^39 + 12 * q^40 - 56 * q^41 + 16 * q^42 + 64 * q^43 - 40 * q^44 + 140 * q^45 + 24 * q^46 - 24 * q^47 + 18 * q^48 - 6 * q^49 - 36 * q^50 + 16 * q^51 - 20 * q^52 + 4 * q^53 + 8 * q^54 + 48 * q^55 - 16 * q^56 + 62 * q^57 - 116 * q^58 - 84 * q^59 - 64 * q^60 - 164 * q^61 - 96 * q^62 - 58 * q^63 - 6 * q^64 - 148 * q^65 - 8 * q^66 - 216 * q^67 - 12 * q^68 - 70 * q^69 - 96 * q^70 - 48 * q^71 + 6 * q^72 - 220 * q^73 - 68 * q^74 - 328 * q^75 + 8 * q^76 - 192 * q^77 - 170 * q^78 - 172 * q^79 - 20 * q^80 + 6 * q^81 - 124 * q^82 - 84 * q^83 - 114 * q^84 - 68 * q^85 - 40 * q^86 - 190 * q^87 - 40 * q^88 - 52 * q^89 - 108 * q^90 - 88 * q^91 - 24 * q^92 + 40 * q^93 - 160 * q^94 + 144 * q^95 + 18 * q^96 + 820 * q^97 + 466 * q^98 + 202 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3450))\)

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
3450.2.a	\(\chi_{3450}(1, \cdot)\)	3450.2.a.a	1	1
		3450.2.a.b	1
		3450.2.a.c	1
		3450.2.a.d	1
		3450.2.a.e	1
		3450.2.a.f	1
		3450.2.a.g	1
		3450.2.a.h	1
		3450.2.a.i	1
		3450.2.a.j	1
		3450.2.a.k	1
		3450.2.a.l	1
		3450.2.a.m	1
		3450.2.a.n	1
		3450.2.a.o	1
		3450.2.a.p	1
		3450.2.a.q	1
		3450.2.a.r	1
		3450.2.a.s	1
		3450.2.a.t	1
		3450.2.a.u	1
		3450.2.a.v	1
		3450.2.a.w	1
		3450.2.a.x	1
		3450.2.a.y	1
		3450.2.a.z	1
		3450.2.a.ba	1
		3450.2.a.bb	1
		3450.2.a.bc	2
		3450.2.a.bd	2
		3450.2.a.be	2
		3450.2.a.bf	2
		3450.2.a.bg	2
		3450.2.a.bh	2
		3450.2.a.bi	2
		3450.2.a.bj	2
		3450.2.a.bk	2
		3450.2.a.bl	2
		3450.2.a.bm	2
		3450.2.a.bn	2
		3450.2.a.bo	3
		3450.2.a.bp	3
		3450.2.a.bq	3
		3450.2.a.br	3
		3450.2.a.bs	3
		3450.2.a.bt	3
3450.2.d	\(\chi_{3450}(2899, \cdot)\)	3450.2.d.a	2	1
		3450.2.d.b	2
		3450.2.d.c	2
		3450.2.d.d	2
		3450.2.d.e	2
		3450.2.d.f	2
		3450.2.d.g	2
		3450.2.d.h	2
		3450.2.d.i	2
		3450.2.d.j	2
		3450.2.d.k	2
		3450.2.d.l	2
		3450.2.d.m	2
		3450.2.d.n	2
		3450.2.d.o	2
		3450.2.d.p	2
		3450.2.d.q	2
		3450.2.d.r	2
		3450.2.d.s	2
		3450.2.d.t	2
		3450.2.d.u	2
		3450.2.d.v	4
		3450.2.d.w	4
		3450.2.d.x	4
		3450.2.d.y	4
		3450.2.d.z	4
		3450.2.d.ba	6
3450.2.e	\(\chi_{3450}(551, \cdot)\)	n/a	152	1
3450.2.h	\(\chi_{3450}(3449, \cdot)\)	n/a	144	1
3450.2.i	\(\chi_{3450}(2393, \cdot)\)	n/a	264	2
3450.2.j	\(\chi_{3450}(643, \cdot)\)	n/a	144	2
3450.2.m	\(\chi_{3450}(691, \cdot)\)	n/a	448	4
3450.2.n	\(\chi_{3450}(1241, \cdot)\)	n/a	960	4
3450.2.o	\(\chi_{3450}(139, \cdot)\)	n/a	432	4
3450.2.r	\(\chi_{3450}(689, \cdot)\)	n/a	960	4
3450.2.u	\(\chi_{3450}(151, \cdot)\)	n/a	760	10
3450.2.x	\(\chi_{3450}(367, \cdot)\)	n/a	960	8
3450.2.y	\(\chi_{3450}(47, \cdot)\)	n/a	1760	8
3450.2.z	\(\chi_{3450}(149, \cdot)\)	n/a	1440	10
3450.2.bc	\(\chi_{3450}(251, \cdot)\)	n/a	1520	10
3450.2.bd	\(\chi_{3450}(49, \cdot)\)	n/a	720	10
3450.2.bi	\(\chi_{3450}(7, \cdot)\)	n/a	1440	20
3450.2.bj	\(\chi_{3450}(257, \cdot)\)	n/a	2880	20
3450.2.bk	\(\chi_{3450}(31, \cdot)\)	n/a	4800	40
3450.2.bn	\(\chi_{3450}(89, \cdot)\)	n/a	9600	40
3450.2.bq	\(\chi_{3450}(169, \cdot)\)	n/a	4800	40
3450.2.br	\(\chi_{3450}(11, \cdot)\)	n/a	9600	40
3450.2.bs	\(\chi_{3450}(77, \cdot)\)	n/a	19200	80
3450.2.bt	\(\chi_{3450}(37, \cdot)\)	n/a	9600	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3450))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3450)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1725))\)\(^{\oplus 2}\)