Space of modular forms of level 2442 and weight 2

• Label: 2442.2
• Level: 2442
• Weight: 2
• Dimension: 40293
• Nonzero newspaces: 36
• Sturm bound: 656640
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 2442 = 2 \cdot 3 \cdot 11 \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(656640\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2442))\).

	Total	New	Old
Modular forms	167040	40293	126747
Cusp forms	161281	40293	120988
Eisenstein series	5759	0	5759

Trace form

40293 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 18 * q^5 + 7 * q^6 + 16 * q^7 - 3 * q^8 + 37 * q^9 + 22 * q^10 + 17 * q^11 + 17 * q^12 - 2 * q^13 + 16 * q^14 + 42 * q^15 - 3 * q^16 + 26 * q^17 + 7 * q^18 - 18 * q^20 + 16 * q^21 - 23 * q^22 - 32 * q^23 - 13 * q^24 - 13 * q^25 - 6 * q^26 - 39 * q^27 + 24 * q^28 + 94 * q^29 + 66 * q^30 + 376 * q^31 - 3 * q^32 - 41 * q^33 + 234 * q^34 + 328 * q^35 + 23 * q^36 + 261 * q^37 + 84 * q^38 + 106 * q^39 + 162 * q^40 + 346 * q^41 + 100 * q^42 + 276 * q^43 + 17 * q^44 - 18 * q^45 + 296 * q^46 + 160 * q^47 + 21 * q^48 + 261 * q^49 + 23 * q^50 + 56 * q^51 + 38 * q^52 - 42 * q^53 + 17 * q^54 + 62 * q^55 - 24 * q^56 - 50 * q^57 + 70 * q^58 + 84 * q^59 + 22 * q^60 + 194 * q^61 + 24 * q^62 + 212 * q^63 - 3 * q^64 + 312 * q^65 + 97 * q^66 + 140 * q^67 + 26 * q^68 + 276 * q^69 + 16 * q^70 + 232 * q^71 + 37 * q^72 + 226 * q^73 - 35 * q^74 + 357 * q^75 - 20 * q^76 + 120 * q^77 + 38 * q^78 + 168 * q^79 + 22 * q^80 + 365 * q^81 - 106 * q^82 + 12 * q^83 - 24 * q^84 + 120 * q^85 - 12 * q^86 + 126 * q^87 + 17 * q^88 + 30 * q^89 - 38 * q^90 - 272 * q^91 - 72 * q^92 - 252 * q^93 - 224 * q^94 - 240 * q^95 - 3 * q^96 - 234 * q^97 - 171 * q^98 - 263 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2442))\)

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
2442.2.a	\(\chi_{2442}(1, \cdot)\)	2442.2.a.a	1	1
		2442.2.a.b	1
		2442.2.a.c	1
		2442.2.a.d	1
		2442.2.a.e	1
		2442.2.a.f	1
		2442.2.a.g	1
		2442.2.a.h	1
		2442.2.a.i	1
		2442.2.a.j	2
		2442.2.a.k	2
		2442.2.a.l	2
		2442.2.a.m	2
		2442.2.a.n	2
		2442.2.a.o	3
		2442.2.a.p	3
		2442.2.a.q	3
		2442.2.a.r	3
		2442.2.a.s	3
		2442.2.a.t	3
		2442.2.a.u	4
		2442.2.a.v	4
		2442.2.a.w	5
		2442.2.a.x	5
		2442.2.a.y	6
2442.2.b	\(\chi_{2442}(593, \cdot)\)	n/a	144	1
2442.2.d	\(\chi_{2442}(1849, \cdot)\)	2442.2.d.a	2	1
		2442.2.d.b	2
		2442.2.d.c	2
		2442.2.d.d	12
		2442.2.d.e	14
		2442.2.d.f	16
		2442.2.d.g	16
2442.2.g	\(\chi_{2442}(2441, \cdot)\)	n/a	152	1
2442.2.i	\(\chi_{2442}(1321, \cdot)\)	n/a	136	2
2442.2.k	\(\chi_{2442}(43, \cdot)\)	n/a	152	2
2442.2.m	\(\chi_{2442}(1079, \cdot)\)	n/a	248	2
2442.2.n	\(\chi_{2442}(223, \cdot)\)	n/a	288	4
2442.2.p	\(\chi_{2442}(989, \cdot)\)	n/a	304	2
2442.2.s	\(\chi_{2442}(397, \cdot)\)	n/a	128	2
2442.2.u	\(\chi_{2442}(1913, \cdot)\)	n/a	304	2
2442.2.v	\(\chi_{2442}(793, \cdot)\)	n/a	384	6
2442.2.x	\(\chi_{2442}(887, \cdot)\)	n/a	608	4
2442.2.ba	\(\chi_{2442}(295, \cdot)\)	n/a	304	4
2442.2.bc	\(\chi_{2442}(149, \cdot)\)	n/a	576	4
2442.2.bd	\(\chi_{2442}(23, \cdot)\)	n/a	496	4
2442.2.bf	\(\chi_{2442}(637, \cdot)\)	n/a	304	4
2442.2.bh	\(\chi_{2442}(433, \cdot)\)	n/a	608	8
2442.2.bj	\(\chi_{2442}(65, \cdot)\)	n/a	912	6
2442.2.bm	\(\chi_{2442}(197, \cdot)\)	n/a	912	6
2442.2.bn	\(\chi_{2442}(67, \cdot)\)	n/a	360	6
2442.2.bp	\(\chi_{2442}(179, \cdot)\)	n/a	1216	8
2442.2.br	\(\chi_{2442}(475, \cdot)\)	n/a	608	8
2442.2.bt	\(\chi_{2442}(359, \cdot)\)	n/a	1216	8
2442.2.bv	\(\chi_{2442}(619, \cdot)\)	n/a	608	8
2442.2.by	\(\chi_{2442}(101, \cdot)\)	n/a	1216	8
2442.2.cb	\(\chi_{2442}(109, \cdot)\)	n/a	912	12
2442.2.cc	\(\chi_{2442}(89, \cdot)\)	n/a	1536	12
2442.2.ce	\(\chi_{2442}(49, \cdot)\)	n/a	1824	24
2442.2.cg	\(\chi_{2442}(193, \cdot)\)	n/a	1216	16
2442.2.ci	\(\chi_{2442}(119, \cdot)\)	n/a	2432	16
2442.2.ck	\(\chi_{2442}(41, \cdot)\)	n/a	3648	24
2442.2.cn	\(\chi_{2442}(25, \cdot)\)	n/a	1824	24
2442.2.co	\(\chi_{2442}(83, \cdot)\)	n/a	3648	24
2442.2.cr	\(\chi_{2442}(5, \cdot)\)	n/a	7296	48
2442.2.cs	\(\chi_{2442}(13, \cdot)\)	n/a	3648	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2442))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2442)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(407))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(814))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1221))\)\(^{\oplus 2}\)