Space of modular forms of level 2254 and weight 2

• Label: 2254.2
• Level: 2254
• Weight: 2
• Dimension: 49464
• Nonzero newspaces: 16
• Sturm bound: 620928
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(620928\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2254))\).

	Total	New	Old
Modular forms	157872	49464	108408
Cusp forms	152593	49464	103129
Eisenstein series	5279	0	5279

Trace form

49464 * q - 2 * q^2 + 6 * q^4 + 12 * q^5 + 16 * q^6 + 16 * q^7 - 2 * q^8 + 30 * q^9 + 12 * q^10 + 24 * q^11 + 12 * q^13 + 12 * q^14 + 70 * q^15 + 6 * q^16 + 82 * q^17 + 66 * q^18 + 70 * q^19 + 34 * q^20 + 52 * q^21 + 46 * q^22 + 68 * q^23 + 16 * q^24 + 86 * q^25 + 66 * q^26 + 162 * q^27 + 16 * q^28 + 58 * q^29 + 92 * q^30 + 70 * q^31 - 2 * q^32 + 118 * q^33 + 12 * q^34 + 84 * q^35 + 30 * q^36 + 16 * q^37 - 52 * q^38 - 8 * q^39 - 72 * q^40 - 38 * q^41 - 108 * q^42 - 4 * q^43 - 60 * q^44 - 198 * q^45 - 102 * q^46 - 76 * q^47 - 28 * q^48 - 236 * q^49 - 86 * q^50 - 196 * q^51 - 16 * q^52 - 14 * q^53 - 166 * q^54 - 188 * q^55 - 72 * q^56 + 86 * q^57 - 40 * q^58 + 38 * q^59 - 14 * q^60 + 48 * q^61 + 62 * q^62 + 72 * q^63 + 6 * q^64 + 322 * q^65 + 184 * q^66 + 164 * q^67 + 104 * q^68 + 206 * q^69 + 84 * q^70 + 254 * q^71 + 66 * q^72 + 200 * q^73 + 156 * q^74 + 464 * q^75 + 48 * q^76 + 168 * q^77 + 146 * q^78 + 302 * q^79 + 34 * q^80 + 162 * q^81 + 104 * q^82 + 64 * q^83 + 52 * q^84 + 114 * q^85 + 78 * q^86 + 18 * q^87 + 24 * q^88 + 10 * q^89 + 156 * q^90 + 20 * q^91 + 24 * q^92 - 216 * q^93 + 144 * q^94 - 30 * q^95 + 16 * q^96 + 76 * q^97 + 96 * q^98 + 152 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2254))\)

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
2254.2.a	\(\chi_{2254}(1, \cdot)\)	2254.2.a.a	1	1
		2254.2.a.b	1
		2254.2.a.c	1
		2254.2.a.d	1
		2254.2.a.e	1
		2254.2.a.f	1
		2254.2.a.g	1
		2254.2.a.h	2
		2254.2.a.i	2
		2254.2.a.j	2
		2254.2.a.k	2
		2254.2.a.l	2
		2254.2.a.m	2
		2254.2.a.n	2
		2254.2.a.o	2
		2254.2.a.p	3
		2254.2.a.q	4
		2254.2.a.r	4
		2254.2.a.s	4
		2254.2.a.t	4
		2254.2.a.u	4
		2254.2.a.v	4
		2254.2.a.w	4
		2254.2.a.x	4
		2254.2.a.y	4
		2254.2.a.z	4
		2254.2.a.ba	4
		2254.2.a.bb	6
2254.2.c	\(\chi_{2254}(2253, \cdot)\)	2254.2.c.a	8	1
		2254.2.c.b	16
		2254.2.c.c	16
		2254.2.c.d	16
		2254.2.c.e	24
2254.2.e	\(\chi_{2254}(1059, \cdot)\)	n/a	144	2
2254.2.g	\(\chi_{2254}(1011, \cdot)\)	n/a	160	2
2254.2.i	\(\chi_{2254}(323, \cdot)\)	n/a	600	6
2254.2.j	\(\chi_{2254}(197, \cdot)\)	n/a	820	10
2254.2.l	\(\chi_{2254}(321, \cdot)\)	n/a	672	6
2254.2.n	\(\chi_{2254}(93, \cdot)\)	n/a	1248	12
2254.2.p	\(\chi_{2254}(97, \cdot)\)	n/a	800	10
2254.2.r	\(\chi_{2254}(165, \cdot)\)	n/a	1600	20
2254.2.t	\(\chi_{2254}(45, \cdot)\)	n/a	1344	12
2254.2.w	\(\chi_{2254}(19, \cdot)\)	n/a	1600	20
2254.2.y	\(\chi_{2254}(29, \cdot)\)	n/a	6720	60
2254.2.ba	\(\chi_{2254}(83, \cdot)\)	n/a	6720	60
2254.2.bc	\(\chi_{2254}(9, \cdot)\)	n/a	13440	120
2254.2.be	\(\chi_{2254}(5, \cdot)\)	n/a	13440	120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2254))\) into lower level spaces

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