Space of modular forms of level 1666 and weight 2

• Label: 1666.2
• Level: 1666
• Weight: 2
• Dimension: 26894
• Nonzero newspaces: 20
• Sturm bound: 338688
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(338688\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1666))\).

	Total	New	Old
Modular forms	86592	26894	59698
Cusp forms	82753	26894	55859
Eisenstein series	3839	0	3839

Trace form

26894 * q - 2 * q^2 + 6 * q^4 + 12 * q^5 + 16 * q^6 + 16 * q^7 - 2 * q^8 + 30 * q^9 + 16 * q^10 + 40 * q^11 + 8 * q^12 + 28 * q^13 + 12 * q^14 + 96 * q^15 + 10 * q^16 + 46 * q^17 + 54 * q^18 + 64 * q^19 + 16 * q^20 + 52 * q^21 + 40 * q^22 + 64 * q^23 + 24 * q^24 + 78 * q^25 + 48 * q^26 + 120 * q^27 + 16 * q^28 + 56 * q^29 + 48 * q^30 + 80 * q^31 - 2 * q^32 + 128 * q^33 + 6 * q^34 + 84 * q^35 + 30 * q^36 + 4 * q^37 - 44 * q^38 + 12 * q^39 - 72 * q^40 + 8 * q^41 - 108 * q^42 + 8 * q^43 - 28 * q^44 - 180 * q^45 - 172 * q^46 - 40 * q^47 - 28 * q^48 - 236 * q^49 - 30 * q^50 - 56 * q^51 + 16 * q^52 + 32 * q^53 - 132 * q^54 - 196 * q^55 - 72 * q^56 + 64 * q^57 - 52 * q^58 + 8 * q^59 - 4 * q^60 + 8 * q^61 + 44 * q^62 + 72 * q^63 + 6 * q^64 + 204 * q^65 + 104 * q^66 + 136 * q^67 + 34 * q^68 + 256 * q^69 + 84 * q^70 + 192 * q^71 + 42 * q^72 + 240 * q^73 + 104 * q^74 + 400 * q^75 + 48 * q^76 + 168 * q^77 + 144 * q^78 + 272 * q^79 + 28 * q^80 + 134 * q^81 + 128 * q^82 + 48 * q^83 + 52 * q^84 + 156 * q^85 + 88 * q^86 + 96 * q^87 + 56 * q^88 + 84 * q^89 + 224 * q^90 + 20 * q^91 + 64 * q^92 - 88 * q^93 + 208 * q^94 + 48 * q^95 + 16 * q^96 + 84 * q^97 + 96 * q^98 - 224 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1666))\)

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
1666.2.a	\(\chi_{1666}(1, \cdot)\)	1666.2.a.a	1	1
		1666.2.a.b	1
		1666.2.a.c	1
		1666.2.a.d	1
		1666.2.a.e	1
		1666.2.a.f	1
		1666.2.a.g	1
		1666.2.a.h	1
		1666.2.a.i	1
		1666.2.a.j	1
		1666.2.a.k	1
		1666.2.a.l	1
		1666.2.a.m	1
		1666.2.a.n	1
		1666.2.a.o	2
		1666.2.a.p	2
		1666.2.a.q	2
		1666.2.a.r	2
		1666.2.a.s	2
		1666.2.a.t	3
		1666.2.a.u	3
		1666.2.a.v	4
		1666.2.a.w	4
		1666.2.a.x	4
		1666.2.a.y	4
		1666.2.a.z	5
		1666.2.a.ba	5
1666.2.b	\(\chi_{1666}(883, \cdot)\)	1666.2.b.a	2	1
		1666.2.b.b	2
		1666.2.b.c	2
		1666.2.b.d	2
		1666.2.b.e	2
		1666.2.b.f	2
		1666.2.b.g	4
		1666.2.b.h	4
		1666.2.b.i	4
		1666.2.b.j	4
		1666.2.b.k	6
		1666.2.b.l	6
		1666.2.b.m	6
		1666.2.b.n	8
		1666.2.b.o	8
1666.2.e	\(\chi_{1666}(851, \cdot)\)	n/a	104	2
1666.2.g	\(\chi_{1666}(1177, \cdot)\)	n/a	124	2
1666.2.j	\(\chi_{1666}(67, \cdot)\)	n/a	120	2
1666.2.k	\(\chi_{1666}(239, \cdot)\)	n/a	432	6
1666.2.l	\(\chi_{1666}(393, \cdot)\)	n/a	244	4
1666.2.o	\(\chi_{1666}(361, \cdot)\)	n/a	240	4
1666.2.r	\(\chi_{1666}(169, \cdot)\)	n/a	504	6
1666.2.t	\(\chi_{1666}(97, \cdot)\)	n/a	480	8
1666.2.u	\(\chi_{1666}(137, \cdot)\)	n/a	912	12
1666.2.v	\(\chi_{1666}(263, \cdot)\)	n/a	480	8
1666.2.x	\(\chi_{1666}(183, \cdot)\)	n/a	1008	12
1666.2.z	\(\chi_{1666}(135, \cdot)\)	n/a	1008	12
1666.2.bc	\(\chi_{1666}(31, \cdot)\)	n/a	960	16
1666.2.bf	\(\chi_{1666}(15, \cdot)\)	n/a	2016	24
1666.2.bg	\(\chi_{1666}(81, \cdot)\)	n/a	2016	24
1666.2.bi	\(\chi_{1666}(27, \cdot)\)	n/a	4032	48
1666.2.bl	\(\chi_{1666}(9, \cdot)\)	n/a	4032	48
1666.2.bn	\(\chi_{1666}(3, \cdot)\)	n/a	8064	96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1666))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1666)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(833))\)\(^{\oplus 2}\)