Space of modular forms of level 2254 and weight 4

• Label: 2254.4
• Level: 2254
• Weight: 4
• Dimension: 148398
• Nonzero newspaces: 16
• Sturm bound: 1241856
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(1241856\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2254))\).

	Total	New	Old
Modular forms	468336	148398	319938
Cusp forms	463056	148398	314658
Eisenstein series	5280	0	5280

Trace form

148398 * q + 48 * q^3 - 96 * q^5 - 144 * q^6 - 96 * q^7 + 168 * q^9 + 144 * q^10 + 168 * q^11 + 192 * q^12 + 264 * q^13 + 264 * q^14 + 700 * q^15 - 424 * q^17 - 760 * q^18 - 460 * q^19 - 832 * q^20 - 144 * q^21 - 1348 * q^22 - 1556 * q^23 - 192 * q^24 + 136 * q^25 + 1172 * q^26 + 2172 * q^27 + 240 * q^28 + 2744 * q^29 + 2168 * q^30 + 1940 * q^31 - 344 * q^33 - 1632 * q^34 - 840 * q^35 - 672 * q^36 - 8052 * q^37 - 4776 * q^38 - 9372 * q^39 - 1440 * q^40 - 5062 * q^41 + 1656 * q^42 - 756 * q^43 + 3024 * q^44 + 11838 * q^45 + 4956 * q^46 + 5764 * q^47 + 960 * q^48 + 15948 * q^49 + 7824 * q^50 + 17988 * q^51 + 2256 * q^52 + 10154 * q^53 + 7084 * q^54 + 14844 * q^55 - 576 * q^56 + 5268 * q^57 - 7224 * q^58 - 6522 * q^59 - 8984 * q^60 - 18864 * q^61 - 12492 * q^62 - 18240 * q^63 + 1536 * q^64 - 16688 * q^65 - 6992 * q^66 - 11136 * q^67 - 5392 * q^68 - 10144 * q^69 - 1512 * q^70 - 9988 * q^71 - 5152 * q^72 - 4488 * q^73 + 2704 * q^74 + 914 * q^75 + 5856 * q^76 + 4452 * q^77 + 6060 * q^78 + 9326 * q^79 - 128 * q^80 - 20484 * q^81 + 1080 * q^82 - 10054 * q^83 - 1824 * q^84 - 1054 * q^85 + 8596 * q^86 + 162 * q^87 + 5376 * q^88 + 11570 * q^89 + 9552 * q^90 + 11052 * q^91 - 864 * q^92 + 39984 * q^93 - 3264 * q^94 + 24720 * q^95 - 768 * q^96 + 10730 * q^97 - 5280 * q^98 + 28542 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2254))\)

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
2254.4.a	\(\chi_{2254}(1, \cdot)\)	2254.4.a.a	1	1
		2254.4.a.b	1
		2254.4.a.c	2
		2254.4.a.d	2
		2254.4.a.e	2
		2254.4.a.f	2
		2254.4.a.g	2
		2254.4.a.h	3
		2254.4.a.i	3
		2254.4.a.j	4
		2254.4.a.k	5
		2254.4.a.l	5
		2254.4.a.m	6
		2254.4.a.n	6
		2254.4.a.o	8
		2254.4.a.p	8
		2254.4.a.q	10
		2254.4.a.r	11
		2254.4.a.s	11
		2254.4.a.t	11
		2254.4.a.u	11
		2254.4.a.v	11
		2254.4.a.w	11
		2254.4.a.x	11
		2254.4.a.y	11
		2254.4.a.z	14
		2254.4.a.ba	16
		2254.4.a.bb	18
		2254.4.a.bc	20
2254.4.c	\(\chi_{2254}(2253, \cdot)\)	n/a	240	1
2254.4.e	\(\chi_{2254}(1059, \cdot)\)	n/a	440	2
2254.4.g	\(\chi_{2254}(1011, \cdot)\)	n/a	480	2
2254.4.i	\(\chi_{2254}(323, \cdot)\)	n/a	1848	6
2254.4.j	\(\chi_{2254}(197, \cdot)\)	n/a	2460	10
2254.4.l	\(\chi_{2254}(321, \cdot)\)	n/a	2016	6
2254.4.n	\(\chi_{2254}(93, \cdot)\)	n/a	3696	12
2254.4.p	\(\chi_{2254}(97, \cdot)\)	n/a	2400	10
2254.4.r	\(\chi_{2254}(165, \cdot)\)	n/a	4800	20
2254.4.t	\(\chi_{2254}(45, \cdot)\)	n/a	4032	12
2254.4.w	\(\chi_{2254}(19, \cdot)\)	n/a	4800	20
2254.4.y	\(\chi_{2254}(29, \cdot)\)	n/a	20160	60
2254.4.ba	\(\chi_{2254}(83, \cdot)\)	n/a	20160	60
2254.4.bc	\(\chi_{2254}(9, \cdot)\)	n/a	40320	120
2254.4.be	\(\chi_{2254}(5, \cdot)\)	n/a	40320	120

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2254))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2254)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1127))\)\(^{\oplus 2}\)