Space of modular forms of level 3042 and weight 2

• Label: 3042.2
• Level: 3042
• Weight: 2
• Dimension: 66635
• Nonzero newspaces: 30
• Sturm bound: 1022112
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(1022112\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3042))\).

	Total	New	Old
Modular forms	259176	66635	192541
Cusp forms	251881	66635	185246
Eisenstein series	7295	0	7295

Trace form

66635 * q - q^2 - 3 * q^3 - q^4 + 3 * q^6 - 10 * q^7 - 4 * q^8 + 3 * q^9 - 30 * q^10 - 21 * q^11 - 24 * q^13 - 26 * q^14 - 9 * q^16 - 36 * q^17 - 6 * q^18 - 58 * q^19 - 6 * q^20 + 6 * q^21 + 3 * q^22 - 18 * q^23 - 3 * q^24 - 25 * q^25 + 28 * q^28 + 108 * q^29 + 96 * q^30 + 148 * q^31 - q^32 + 135 * q^33 + 147 * q^34 + 336 * q^35 + 99 * q^36 + 154 * q^37 + 217 * q^38 + 96 * q^39 + 273 * q^41 + 144 * q^42 + 137 * q^43 + 138 * q^44 + 240 * q^45 + 132 * q^46 + 198 * q^47 + 3 * q^48 + 163 * q^49 + 143 * q^50 + 105 * q^51 + 9 * q^52 - 48 * q^53 + 9 * q^54 - 120 * q^55 - 26 * q^56 + 3 * q^57 - 60 * q^58 - 99 * q^59 - 86 * q^61 - 80 * q^62 + 84 * q^63 - 4 * q^64 + 57 * q^65 + 35 * q^67 - 3 * q^68 + 144 * q^69 - 72 * q^70 + 216 * q^71 + 3 * q^72 + 230 * q^73 - 74 * q^74 + 225 * q^75 - 55 * q^76 + 150 * q^77 + 4 * q^79 - 6 * q^80 + 183 * q^81 - 84 * q^82 + 276 * q^83 - 6 * q^84 + 138 * q^85 - 47 * q^86 + 210 * q^87 + 3 * q^88 + 108 * q^89 + 20 * q^91 - 42 * q^92 + 144 * q^93 - 114 * q^94 + 48 * q^95 - 125 * q^97 - 198 * q^98 - 270 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3042))\)

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
3042.2.a	\(\chi_{3042}(1, \cdot)\)	3042.2.a.a	1	1
		3042.2.a.b	1
		3042.2.a.c	1
		3042.2.a.d	1
		3042.2.a.e	1
		3042.2.a.f	1
		3042.2.a.g	1
		3042.2.a.h	1
		3042.2.a.i	1
		3042.2.a.j	1
		3042.2.a.k	1
		3042.2.a.l	1
		3042.2.a.m	1
		3042.2.a.n	1
		3042.2.a.o	1
		3042.2.a.p	2
		3042.2.a.q	2
		3042.2.a.r	2
		3042.2.a.s	2
		3042.2.a.t	2
		3042.2.a.u	2
		3042.2.a.v	2
		3042.2.a.w	2
		3042.2.a.x	2
		3042.2.a.y	2
		3042.2.a.z	3
		3042.2.a.ba	3
		3042.2.a.bb	3
		3042.2.a.bc	3
		3042.2.a.bd	3
		3042.2.a.be	3
		3042.2.a.bf	3
		3042.2.a.bg	3
		3042.2.a.bh	3
		3042.2.a.bi	3
3042.2.b	\(\chi_{3042}(1351, \cdot)\)	3042.2.b.a	2	1
		3042.2.b.b	2
		3042.2.b.c	2
		3042.2.b.d	2
		3042.2.b.e	2
		3042.2.b.f	2
		3042.2.b.g	2
		3042.2.b.h	2
		3042.2.b.i	4
		3042.2.b.j	4
		3042.2.b.k	4
		3042.2.b.l	4
		3042.2.b.m	4
		3042.2.b.n	6
		3042.2.b.o	6
		3042.2.b.p	6
		3042.2.b.q	6
		3042.2.b.r	6
3042.2.e	\(\chi_{3042}(1015, \cdot)\)	n/a	310	2
3042.2.f	\(\chi_{3042}(1543, \cdot)\)	n/a	308	2
3042.2.g	\(\chi_{3042}(529, \cdot)\)	n/a	308	2
3042.2.h	\(\chi_{3042}(991, \cdot)\)	n/a	126	2
3042.2.j	\(\chi_{3042}(2267, \cdot)\)	n/a	108	2
3042.2.l	\(\chi_{3042}(361, \cdot)\)	n/a	128	2
3042.2.p	\(\chi_{3042}(2389, \cdot)\)	n/a	308	2
3042.2.s	\(\chi_{3042}(823, \cdot)\)	n/a	308	2
3042.2.t	\(\chi_{3042}(337, \cdot)\)	n/a	308	2
3042.2.x	\(\chi_{3042}(89, \cdot)\)	n/a	200	4
3042.2.y	\(\chi_{3042}(587, \cdot)\)	n/a	616	4
3042.2.z	\(\chi_{3042}(695, \cdot)\)	n/a	616	4
3042.2.bd	\(\chi_{3042}(239, \cdot)\)	n/a	616	4
3042.2.be	\(\chi_{3042}(235, \cdot)\)	n/a	900	12
3042.2.bh	\(\chi_{3042}(181, \cdot)\)	n/a	888	12
3042.2.bi	\(\chi_{3042}(55, \cdot)\)	n/a	1848	24
3042.2.bj	\(\chi_{3042}(61, \cdot)\)	n/a	4368	24
3042.2.bk	\(\chi_{3042}(133, \cdot)\)	n/a	4368	24
3042.2.bl	\(\chi_{3042}(79, \cdot)\)	n/a	4368	24
3042.2.bm	\(\chi_{3042}(125, \cdot)\)	n/a	1392	24
3042.2.bq	\(\chi_{3042}(25, \cdot)\)	n/a	4368	24
3042.2.br	\(\chi_{3042}(121, \cdot)\)	n/a	4368	24
3042.2.bu	\(\chi_{3042}(43, \cdot)\)	n/a	4368	24
3042.2.by	\(\chi_{3042}(127, \cdot)\)	n/a	1824	24
3042.2.ca	\(\chi_{3042}(5, \cdot)\)	n/a	8736	48
3042.2.ce	\(\chi_{3042}(11, \cdot)\)	n/a	8736	48
3042.2.cf	\(\chi_{3042}(71, \cdot)\)	n/a	2976	48
3042.2.cg	\(\chi_{3042}(41, \cdot)\)	n/a	8736	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3042))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3042)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1521))\)\(^{\oplus 2}\)