Space of modular forms of level 2178 and weight 2

• Label: 2178.2
• Level: 2178
• Weight: 2
• Dimension: 33917
• Nonzero newspaces: 16
• Sturm bound: 522720
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(522720\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2178))\).

	Total	New	Old
Modular forms	133240	33917	99323
Cusp forms	128121	33917	94204
Eisenstein series	5119	0	5119

Trace form

33917 * q - q^2 - 3 * q^3 - q^4 + 3 * q^6 - 22 * q^7 + 2 * q^8 + 3 * q^9 - 20 * q^10 - 10 * q^11 - 22 * q^13 - 22 * q^14 - q^16 - 46 * q^17 - 6 * q^18 - 32 * q^19 + 6 * q^21 + 46 * q^23 + 17 * q^24 + 85 * q^25 + 124 * q^26 + 120 * q^27 + 64 * q^28 + 154 * q^29 + 120 * q^30 + 104 * q^31 + 29 * q^32 + 100 * q^33 + 123 * q^34 + 280 * q^35 + 23 * q^36 + 112 * q^37 + 181 * q^38 + 120 * q^39 + 60 * q^40 + 151 * q^41 + 80 * q^42 + 61 * q^43 + 5 * q^44 + 40 * q^45 - 52 * q^46 - 74 * q^47 + 3 * q^48 - 117 * q^49 - 35 * q^50 + 29 * q^51 - 42 * q^52 + 84 * q^53 + 9 * q^54 + 10 * q^55 - 2 * q^56 + 163 * q^57 - 86 * q^58 + 147 * q^59 + 12 * q^61 - 68 * q^62 + 148 * q^63 + 2 * q^64 + 120 * q^65 + 135 * q^67 - 37 * q^68 + 160 * q^69 - 80 * q^70 + 136 * q^71 + 3 * q^72 + 62 * q^73 - 36 * q^74 + 125 * q^75 - 19 * q^76 + 80 * q^77 - 6 * q^78 + 64 * q^79 - 20 * q^80 - 89 * q^81 + 68 * q^82 - 222 * q^83 - 166 * q^84 - 60 * q^85 - 269 * q^86 - 382 * q^87 - 10 * q^88 - 348 * q^89 - 400 * q^90 + 288 * q^91 - 174 * q^92 - 400 * q^93 + 46 * q^94 - 540 * q^95 - 35 * q^97 - 276 * q^98 - 320 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2178))\)

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
2178.2.a	\(\chi_{2178}(1, \cdot)\)	2178.2.a.a	1	1
		2178.2.a.b	1
		2178.2.a.c	1
		2178.2.a.d	1
		2178.2.a.e	1
		2178.2.a.f	1
		2178.2.a.g	1
		2178.2.a.h	1
		2178.2.a.i	1
		2178.2.a.j	1
		2178.2.a.k	1
		2178.2.a.l	1
		2178.2.a.m	1
		2178.2.a.n	2
		2178.2.a.o	2
		2178.2.a.p	2
		2178.2.a.q	2
		2178.2.a.r	2
		2178.2.a.s	2
		2178.2.a.t	2
		2178.2.a.u	2
		2178.2.a.v	2
		2178.2.a.w	2
		2178.2.a.x	2
		2178.2.a.y	2
		2178.2.a.z	2
		2178.2.a.ba	2
		2178.2.a.bb	2
		2178.2.a.bc	2
2178.2.b	\(\chi_{2178}(2177, \cdot)\)	2178.2.b.a	2	1
		2178.2.b.b	2
		2178.2.b.c	2
		2178.2.b.d	2
		2178.2.b.e	2
		2178.2.b.f	2
		2178.2.b.g	4
		2178.2.b.h	4
		2178.2.b.i	8
		2178.2.b.j	8
2178.2.e	\(\chi_{2178}(727, \cdot)\)	n/a	218	2
2178.2.f	\(\chi_{2178}(487, \cdot)\)	n/a	180	4
2178.2.i	\(\chi_{2178}(725, \cdot)\)	n/a	216	2
2178.2.l	\(\chi_{2178}(161, \cdot)\)	n/a	144	4
2178.2.m	\(\chi_{2178}(199, \cdot)\)	n/a	550	10
2178.2.n	\(\chi_{2178}(493, \cdot)\)	n/a	864	8
2178.2.q	\(\chi_{2178}(197, \cdot)\)	n/a	440	10
2178.2.r	\(\chi_{2178}(239, \cdot)\)	n/a	864	8
2178.2.u	\(\chi_{2178}(67, \cdot)\)	n/a	2640	20
2178.2.v	\(\chi_{2178}(37, \cdot)\)	n/a	2200	40
2178.2.w	\(\chi_{2178}(65, \cdot)\)	n/a	2640	20
2178.2.z	\(\chi_{2178}(17, \cdot)\)	n/a	1760	40
2178.2.bc	\(\chi_{2178}(25, \cdot)\)	n/a	10560	80
2178.2.bf	\(\chi_{2178}(29, \cdot)\)	n/a	10560	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2178))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2178)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 2}\)