Space of modular forms of level 1694 and weight 2

• Label: 1694.2
• Level: 1694
• Weight: 2
• Dimension: 27370
• Nonzero newspaces: 16
• Sturm bound: 348480
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(348480\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1694))\).

	Total	New	Old
Modular forms	89040	27370	61670
Cusp forms	85201	27370	57831
Eisenstein series	3839	0	3839

Trace form

27370 * q - 2 * q^2 - 6 * q^3 - 6 * q^5 + 18 * q^6 + 20 * q^7 - 2 * q^8 + 68 * q^9 + 34 * q^10 + 20 * q^11 + 34 * q^12 + 22 * q^13 + 18 * q^14 + 96 * q^15 + 68 * q^17 + 6 * q^18 + 42 * q^19 - 6 * q^20 + 34 * q^21 + 56 * q^23 + 18 * q^24 + 124 * q^25 + 70 * q^26 + 144 * q^27 + 20 * q^28 + 124 * q^29 + 96 * q^30 + 84 * q^31 + 18 * q^32 + 110 * q^33 + 56 * q^34 + 114 * q^35 + 8 * q^36 + 44 * q^37 + 98 * q^38 + 152 * q^39 + 34 * q^40 + 124 * q^41 + 58 * q^42 + 164 * q^43 + 30 * q^44 + 122 * q^45 + 56 * q^46 + 100 * q^47 - 6 * q^48 + 120 * q^49 + 54 * q^50 + 176 * q^51 + 62 * q^52 + 152 * q^53 + 116 * q^54 + 140 * q^55 - 2 * q^56 + 256 * q^57 + 136 * q^58 + 194 * q^59 + 56 * q^60 + 106 * q^61 - 28 * q^62 - 132 * q^63 - 44 * q^65 - 120 * q^66 + 48 * q^67 - 52 * q^68 - 256 * q^69 - 286 * q^70 - 232 * q^71 - 174 * q^72 - 192 * q^73 - 200 * q^74 - 614 * q^75 - 98 * q^76 - 100 * q^77 - 384 * q^78 - 232 * q^79 - 86 * q^80 - 552 * q^81 - 148 * q^82 - 190 * q^83 - 166 * q^84 - 148 * q^85 - 152 * q^86 - 308 * q^87 - 40 * q^88 - 16 * q^89 - 198 * q^90 - 178 * q^91 + 96 * q^92 + 40 * q^93 + 84 * q^94 + 200 * q^95 - 2 * q^96 + 272 * q^97 + 18 * q^98 + 260 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1694))\)

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
1694.2.a	\(\chi_{1694}(1, \cdot)\)	1694.2.a.a	1	1
		1694.2.a.b	1
		1694.2.a.c	1
		1694.2.a.d	1
		1694.2.a.e	1
		1694.2.a.f	1
		1694.2.a.g	1
		1694.2.a.h	1
		1694.2.a.i	1
		1694.2.a.j	1
		1694.2.a.k	2
		1694.2.a.l	2
		1694.2.a.m	2
		1694.2.a.n	2
		1694.2.a.o	2
		1694.2.a.p	2
		1694.2.a.q	2
		1694.2.a.r	2
		1694.2.a.s	2
		1694.2.a.t	2
		1694.2.a.u	2
		1694.2.a.v	3
		1694.2.a.w	3
		1694.2.a.x	4
		1694.2.a.y	4
		1694.2.a.z	4
		1694.2.a.ba	4
1694.2.c	\(\chi_{1694}(1693, \cdot)\)	1694.2.c.a	8	1
		1694.2.c.b	32
		1694.2.c.c	32
1694.2.e	\(\chi_{1694}(485, \cdot)\)	n/a	144	2
1694.2.f	\(\chi_{1694}(323, \cdot)\)	n/a	216	4
1694.2.i	\(\chi_{1694}(241, \cdot)\)	n/a	144	2
1694.2.k	\(\chi_{1694}(475, \cdot)\)	n/a	288	4
1694.2.m	\(\chi_{1694}(155, \cdot)\)	n/a	660	10
1694.2.n	\(\chi_{1694}(9, \cdot)\)	n/a	576	8
1694.2.o	\(\chi_{1694}(153, \cdot)\)	n/a	880	10
1694.2.r	\(\chi_{1694}(215, \cdot)\)	n/a	576	8
1694.2.u	\(\chi_{1694}(23, \cdot)\)	n/a	1760	20
1694.2.v	\(\chi_{1694}(15, \cdot)\)	n/a	2640	40
1694.2.x	\(\chi_{1694}(87, \cdot)\)	n/a	1760	20
1694.2.bb	\(\chi_{1694}(13, \cdot)\)	n/a	3520	40
1694.2.bc	\(\chi_{1694}(25, \cdot)\)	n/a	7040	80
1694.2.be	\(\chi_{1694}(17, \cdot)\)	n/a	7040	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1694))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1694)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 2}\)