Space of modular forms of level 1210 and weight 2

• Label: 1210.2
• Level: 1210
• Weight: 2
• Dimension: 13089
• Nonzero newspaces: 12
• Sturm bound: 174240
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(174240\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1210))\).

	Total	New	Old
Modular forms	44840	13089	31751
Cusp forms	42281	13089	29192
Eisenstein series	2559	0	2559

Trace form

13089 * q - q^2 - 4 * q^3 - q^4 - q^5 + 16 * q^6 + 32 * q^7 - q^8 + 67 * q^9 + 19 * q^10 + 20 * q^11 + 36 * q^12 + 26 * q^13 + 32 * q^14 + 56 * q^15 - q^16 + 62 * q^17 + 7 * q^18 + 40 * q^19 - q^20 + 48 * q^21 + 56 * q^23 + 16 * q^24 + 79 * q^25 + 66 * q^26 + 140 * q^27 + 32 * q^28 + 130 * q^29 + 56 * q^30 + 88 * q^31 + 19 * q^32 + 110 * q^33 + 62 * q^34 + 112 * q^35 + 7 * q^36 + 42 * q^37 + 100 * q^38 + 144 * q^39 + 19 * q^40 + 118 * q^41 + 8 * q^42 - 4 * q^43 - 10 * q^44 - 153 * q^45 - 104 * q^46 - 128 * q^47 - 4 * q^48 - 217 * q^49 - 121 * q^50 - 132 * q^51 - 94 * q^52 - 94 * q^53 - 200 * q^54 - 90 * q^55 - 8 * q^56 - 60 * q^57 - 190 * q^58 - 40 * q^59 - 124 * q^60 - 102 * q^61 - 72 * q^62 - 24 * q^63 - q^64 - 54 * q^65 + 40 * q^66 + 52 * q^67 - 18 * q^68 + 184 * q^69 - 8 * q^70 + 248 * q^71 + 67 * q^72 + 166 * q^73 + 42 * q^74 + 176 * q^75 + 20 * q^76 + 160 * q^77 + 104 * q^78 + 120 * q^79 + 19 * q^80 + 419 * q^81 + 98 * q^82 + 176 * q^83 + 128 * q^84 + 202 * q^85 + 216 * q^86 + 280 * q^87 + 20 * q^88 + 230 * q^89 + 167 * q^90 + 208 * q^91 + 96 * q^92 + 152 * q^93 + 192 * q^94 + 40 * q^95 - 4 * q^96 + 42 * q^97 + 123 * q^98 + 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)

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
1210.2.a	\(\chi_{1210}(1, \cdot)\)	1210.2.a.a	1	1
		1210.2.a.b	1
		1210.2.a.c	1
		1210.2.a.d	1
		1210.2.a.e	1
		1210.2.a.f	1
		1210.2.a.g	1
		1210.2.a.h	1
		1210.2.a.i	1
		1210.2.a.j	1
		1210.2.a.k	1
		1210.2.a.l	1
		1210.2.a.m	1
		1210.2.a.n	2
		1210.2.a.o	2
		1210.2.a.p	2
		1210.2.a.q	2
		1210.2.a.r	2
		1210.2.a.s	2
		1210.2.a.t	2
		1210.2.a.u	4
		1210.2.a.v	4
1210.2.b	\(\chi_{1210}(969, \cdot)\)	1210.2.b.a	2	1
		1210.2.b.b	2
		1210.2.b.c	2
		1210.2.b.d	2
		1210.2.b.e	2
		1210.2.b.f	4
		1210.2.b.g	4
		1210.2.b.h	4
		1210.2.b.i	4
		1210.2.b.j	4
		1210.2.b.k	8
		1210.2.b.l	8
		1210.2.b.m	8
1210.2.f	\(\chi_{1210}(483, \cdot)\)	n/a	108	2
1210.2.g	\(\chi_{1210}(81, \cdot)\)	n/a	144	4
1210.2.j	\(\chi_{1210}(9, \cdot)\)	n/a	216	4
1210.2.k	\(\chi_{1210}(111, \cdot)\)	n/a	440	10
1210.2.l	\(\chi_{1210}(233, \cdot)\)	n/a	432	8
1210.2.o	\(\chi_{1210}(89, \cdot)\)	n/a	660	10
1210.2.q	\(\chi_{1210}(43, \cdot)\)	n/a	1320	20
1210.2.s	\(\chi_{1210}(31, \cdot)\)	n/a	1760	40
1210.2.u	\(\chi_{1210}(49, \cdot)\)	n/a	2640	40
1210.2.x	\(\chi_{1210}(7, \cdot)\)	n/a	5280	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1210))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1210)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 2}\)