Space of modular forms of level 1166 and weight 2

• Label: 1166.2
• Level: 1166
• Weight: 2
• Dimension: 13799
• Nonzero newspaces: 12
• Sturm bound: 168480
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 1166 = 2 \cdot 11 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(168480\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1166))\).

	Total	New	Old
Modular forms	43160	13799	29361
Cusp forms	41081	13799	27282
Eisenstein series	2079	0	2079

Trace form

13799 * q + 3 * q^2 + 12 * q^3 + 3 * q^4 + 18 * q^5 + 2 * q^6 + 4 * q^7 + 3 * q^8 - q^9 - 2 * q^10 + 3 * q^11 - 8 * q^12 + 22 * q^13 + 4 * q^14 + 12 * q^15 + 3 * q^16 + 14 * q^17 + 29 * q^18 + 30 * q^19 + 18 * q^20 + 56 * q^21 + 23 * q^22 + 32 * q^23 + 2 * q^24 + 13 * q^25 + 2 * q^26 + 30 * q^27 + 4 * q^28 + 10 * q^29 + 12 * q^30 + 36 * q^31 - 7 * q^32 - 18 * q^33 + 14 * q^34 + 24 * q^35 + 29 * q^36 + 74 * q^37 + 68 * q^39 - 28 * q^40 - 58 * q^41 - 172 * q^42 - 176 * q^43 - 7 * q^44 - 386 * q^45 - 72 * q^46 - 40 * q^47 - 92 * q^48 - 157 * q^49 - 181 * q^50 - 330 * q^51 - 102 * q^52 - 255 * q^53 - 272 * q^54 - 158 * q^55 - 80 * q^56 - 346 * q^57 - 224 * q^58 - 158 * q^59 - 72 * q^60 - 58 * q^61 - 68 * q^62 - 448 * q^63 + 3 * q^64 - 156 * q^65 - 132 * q^66 - 80 * q^67 - 12 * q^68 + 68 * q^69 + 64 * q^70 + 56 * q^71 - q^72 + 102 * q^73 + 74 * q^74 + 142 * q^75 + 40 * q^76 + 24 * q^77 + 88 * q^78 + 140 * q^79 - 2 * q^80 + 93 * q^81 + 56 * q^82 + 122 * q^83 + 16 * q^84 + 104 * q^85 + 2 * q^86 + 56 * q^87 + 3 * q^88 - 20 * q^89 + 54 * q^90 - 72 * q^91 + 12 * q^92 - 84 * q^93 + 24 * q^94 - 68 * q^95 + 12 * q^96 - 338 * q^97 + 81 * q^98 - 221 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1166))\)

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
1166.2.a	\(\chi_{1166}(1, \cdot)\)	1166.2.a.a	1	1
		1166.2.a.b	1
		1166.2.a.c	1
		1166.2.a.d	1
		1166.2.a.e	2
		1166.2.a.f	3
		1166.2.a.g	3
		1166.2.a.h	4
		1166.2.a.i	4
		1166.2.a.j	4
		1166.2.a.k	6
		1166.2.a.l	7
		1166.2.a.m	8
1166.2.c	\(\chi_{1166}(529, \cdot)\)	1166.2.c.a	2	1
		1166.2.c.b	22
		1166.2.c.c	22
1166.2.f	\(\chi_{1166}(659, \cdot)\)	n/a	108	2
1166.2.g	\(\chi_{1166}(213, \cdot)\)	n/a	208	4
1166.2.i	\(\chi_{1166}(317, \cdot)\)	n/a	216	4
1166.2.k	\(\chi_{1166}(89, \cdot)\)	n/a	528	12
1166.2.l	\(\chi_{1166}(83, \cdot)\)	n/a	432	8
1166.2.o	\(\chi_{1166}(199, \cdot)\)	n/a	552	12
1166.2.q	\(\chi_{1166}(21, \cdot)\)	n/a	1296	24
1166.2.s	\(\chi_{1166}(15, \cdot)\)	n/a	2592	48
1166.2.u	\(\chi_{1166}(9, \cdot)\)	n/a	2592	48
1166.2.x	\(\chi_{1166}(19, \cdot)\)	n/a	5184	96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1166))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1166)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(583))\)\(^{\oplus 2}\)