Space of modular forms of level 1701 and weight 2

• Label: 1701.2
• Level: 1701
• Weight: 2
• Dimension: 78528
• Nonzero newspaces: 28
• Sturm bound: 419904
• Trace bound: 65

Defining parameters

Level:	\( N \)	=	\( 1701 = 3^{5} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(419904\)
Trace bound:			\(65\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1701))\).

	Total	New	Old
Modular forms	107244	80448	26796
Cusp forms	102709	78528	24181
Eisenstein series	4535	1920	2615

Trace form

78528 * q - 144 * q^2 - 216 * q^3 - 240 * q^4 - 144 * q^5 - 216 * q^6 - 300 * q^7 - 360 * q^8 - 216 * q^9 - 336 * q^10 - 144 * q^11 - 216 * q^12 - 240 * q^13 - 180 * q^14 - 540 * q^15 - 216 * q^16 - 144 * q^17 - 216 * q^18 - 318 * q^19 - 72 * q^20 - 270 * q^21 - 564 * q^22 - 90 * q^23 - 216 * q^24 - 204 * q^25 - 18 * q^26 - 216 * q^27 - 519 * q^28 - 306 * q^29 - 216 * q^30 - 204 * q^31 - 36 * q^32 - 216 * q^33 - 180 * q^34 - 153 * q^35 - 540 * q^36 - 318 * q^37 - 126 * q^38 - 216 * q^39 - 132 * q^40 - 108 * q^41 - 270 * q^42 - 564 * q^43 - 216 * q^45 - 228 * q^46 - 36 * q^47 - 216 * q^48 - 264 * q^49 - 126 * q^50 - 216 * q^51 - 216 * q^52 - 18 * q^53 - 216 * q^54 - 336 * q^55 - 36 * q^56 - 540 * q^57 - 132 * q^58 - 18 * q^59 - 216 * q^60 - 168 * q^61 + 54 * q^62 - 270 * q^63 - 924 * q^64 - 216 * q^65 - 432 * q^66 - 330 * q^67 - 684 * q^68 - 432 * q^69 - 372 * q^70 - 720 * q^71 - 864 * q^72 - 552 * q^73 - 864 * q^74 - 486 * q^75 - 570 * q^76 - 540 * q^77 - 972 * q^78 - 492 * q^79 - 1494 * q^80 - 432 * q^81 - 876 * q^82 - 504 * q^83 - 648 * q^84 - 792 * q^85 - 864 * q^86 - 648 * q^87 - 498 * q^88 - 540 * q^89 - 648 * q^90 - 492 * q^91 - 1260 * q^92 - 432 * q^93 - 384 * q^94 - 288 * q^95 - 594 * q^96 - 258 * q^97 - 189 * q^98 - 648 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1701))\)

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
1701.2.a	\(\chi_{1701}(1, \cdot)\)	1701.2.a.a	1	1
		1701.2.a.b	1
		1701.2.a.c	1
		1701.2.a.d	1
		1701.2.a.e	1
		1701.2.a.f	1
		1701.2.a.g	1
		1701.2.a.h	1
		1701.2.a.i	1
		1701.2.a.j	1
		1701.2.a.k	2
		1701.2.a.l	2
		1701.2.a.m	2
		1701.2.a.n	3
		1701.2.a.o	3
		1701.2.a.p	4
		1701.2.a.q	4
		1701.2.a.r	4
		1701.2.a.s	4
		1701.2.a.t	4
		1701.2.a.u	6
		1701.2.a.v	6
		1701.2.a.w	9
		1701.2.a.x	9
1701.2.c	\(\chi_{1701}(1700, \cdot)\)	1701.2.c.a	2	1
		1701.2.c.b	2
		1701.2.c.c	2
		1701.2.c.d	2
		1701.2.c.e	12
		1701.2.c.f	12
		1701.2.c.g	16
		1701.2.c.h	48
1701.2.e	\(\chi_{1701}(487, \cdot)\)	n/a	192	2
1701.2.f	\(\chi_{1701}(568, \cdot)\)	n/a	144	2
1701.2.g	\(\chi_{1701}(163, \cdot)\)	n/a	192	2
1701.2.h	\(\chi_{1701}(1297, \cdot)\)	n/a	192	2
1701.2.i	\(\chi_{1701}(80, \cdot)\)	n/a	192	2
1701.2.o	\(\chi_{1701}(566, \cdot)\)	n/a	192	2
1701.2.p	\(\chi_{1701}(971, \cdot)\)	n/a	192	2
1701.2.s	\(\chi_{1701}(647, \cdot)\)	n/a	192	2
1701.2.u	\(\chi_{1701}(109, \cdot)\)	n/a	528	6
1701.2.v	\(\chi_{1701}(190, \cdot)\)	n/a	432	6
1701.2.w	\(\chi_{1701}(298, \cdot)\)	n/a	528	6
1701.2.ba	\(\chi_{1701}(215, \cdot)\)	n/a	528	6
1701.2.bd	\(\chi_{1701}(26, \cdot)\)	n/a	528	6
1701.2.be	\(\chi_{1701}(188, \cdot)\)	n/a	528	6
1701.2.bg	\(\chi_{1701}(100, \cdot)\)	n/a	1260	18
1701.2.bh	\(\chi_{1701}(64, \cdot)\)	n/a	972	18
1701.2.bi	\(\chi_{1701}(37, \cdot)\)	n/a	1260	18
1701.2.bl	\(\chi_{1701}(17, \cdot)\)	n/a	1260	18
1701.2.bm	\(\chi_{1701}(62, \cdot)\)	n/a	1260	18
1701.2.br	\(\chi_{1701}(143, \cdot)\)	n/a	1260	18
1701.2.bs	\(\chi_{1701}(22, \cdot)\)	n/a	8748	54
1701.2.bt	\(\chi_{1701}(25, \cdot)\)	n/a	11556	54
1701.2.bu	\(\chi_{1701}(4, \cdot)\)	n/a	11556	54
1701.2.bx	\(\chi_{1701}(20, \cdot)\)	n/a	11556	54
1701.2.by	\(\chi_{1701}(5, \cdot)\)	n/a	11556	54
1701.2.cd	\(\chi_{1701}(47, \cdot)\)	n/a	11556	54

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1701))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1701)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(567))\)\(^{\oplus 2}\)