Space of modular forms of level 2695 and weight 1

• Label: 2695.1
• Level: 2695
• Weight: 1
• Dimension: 199
• Nonzero newspaces: 9
• Newform subspaces: 30
• Sturm bound: 564480
• Trace bound: 4

Defining parameters

Level:	$N$	=	$2695 = 5 \cdot 7^{2} \cdot 11$
Weight:	$k$	=	$1$
Nonzero newspaces:			$9$
Newform subspaces:			$30$
Sturm bound:			$564480$
Trace bound:			$4$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(\Gamma_1(2695))$.

	Total	New	Old
Modular forms	5108	2817	2291
Cusp forms	308	199	109
Eisenstein series	4800	2618	2182

The following table gives the dimensions of subspaces with specified projective image type.

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	199	0	0	0

Trace form

199 * q + 7 * q^4 + q^5 - q^9 + 3 * q^11 - 12 * q^14 - 6 * q^15 - 11 * q^16 + 7 * q^20 + 5 * q^25 + 8 * q^26 - 8 * q^29 + 2 * q^31 + 8 * q^34 - 49 * q^36 - 2 * q^39 - 15 * q^44 + q^45 - 2 * q^51 - 21 * q^55 - 12 * q^56 - 18 * q^59 + 4 * q^60 - 33 * q^64 + 4 * q^65 - 12 * q^70 - 14 * q^71 + 4 * q^79 - 15 * q^80 + 3 * q^81 - 8 * q^85 - 16 * q^86 + 2 * q^89 - 29 * q^99

Decomposition of $S_{1}^{\mathrm{new}}(\Gamma_1(2695))$

We only show spaces with odd 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
2695.1.d	$\chi_{2695}(736, \cdot)$	None	0	1
2695.1.e	$\chi_{2695}(1959, \cdot)$	None	0	1
2695.1.f	$\chi_{2695}(881, \cdot)$	None	0	1
2695.1.g	$\chi_{2695}(1814, \cdot)$	2695.1.g.a	1	1
		2695.1.g.b	1
		2695.1.g.c	1
		2695.1.g.d	1
		2695.1.g.e	1
		2695.1.g.f	2
		2695.1.g.g	2
		2695.1.g.h	2
		2695.1.g.i	4
2695.1.l	$\chi_{2695}(538, \cdot)$	2695.1.l.a	8	2
		2695.1.l.b	8
2695.1.m	$\chi_{2695}(1618, \cdot)$	None	0	2
2695.1.p	$\chi_{2695}(166, \cdot)$	None	0	2
2695.1.q	$\chi_{2695}(2419, \cdot)$	2695.1.q.a	2	2
		2695.1.q.b	2
		2695.1.q.c	2
		2695.1.q.d	2
		2695.1.q.e	4
		2695.1.q.f	4
		2695.1.q.g	8
2695.1.r	$\chi_{2695}(1341, \cdot)$	None	0	2
2695.1.s	$\chi_{2695}(1244, \cdot)$	None	0	2
2695.1.x	$\chi_{2695}(589, \cdot)$	2695.1.x.a	8	4
2695.1.y	$\chi_{2695}(146, \cdot)$	None	0	4
2695.1.z	$\chi_{2695}(489, \cdot)$	None	0	4
2695.1.ba	$\chi_{2695}(491, \cdot)$	None	0	4
2695.1.bf	$\chi_{2695}(67, \cdot)$	None	0	4
2695.1.bg	$\chi_{2695}(362, \cdot)$	2695.1.bg.a	16	4
		2695.1.bg.b	16
2695.1.bi	$\chi_{2695}(274, \cdot)$	2695.1.bi.a	6	6
		2695.1.bi.b	6
		2695.1.bi.c	12
2695.1.bj	$\chi_{2695}(111, \cdot)$	None	0	6
2695.1.bk	$\chi_{2695}(34, \cdot)$	None	0	6
2695.1.bl	$\chi_{2695}(351, \cdot)$	None	0	6
2695.1.bp	$\chi_{2695}(148, \cdot)$	None	0	8
2695.1.bq	$\chi_{2695}(293, \cdot)$	None	0	8
2695.1.bu	$\chi_{2695}(78, \cdot)$	None	0	12
2695.1.bv	$\chi_{2695}(153, \cdot)$	None	0	12
2695.1.ca	$\chi_{2695}(509, \cdot)$	2695.1.ca.a	8	8
		2695.1.ca.b	8
2695.1.cb	$\chi_{2695}(116, \cdot)$	None	0	8
2695.1.cc	$\chi_{2695}(79, \cdot)$	2695.1.cc.a	16	8
2695.1.cd	$\chi_{2695}(31, \cdot)$	None	0	8
2695.1.ci	$\chi_{2695}(89, \cdot)$	None	0	12
2695.1.cj	$\chi_{2695}(186, \cdot)$	None	0	12
2695.1.ck	$\chi_{2695}(109, \cdot)$	2695.1.ck.a	12	12
		2695.1.ck.b	12
		2695.1.ck.c	24
2695.1.cl	$\chi_{2695}(551, \cdot)$	None	0	12
2695.1.cn	$\chi_{2695}(68, \cdot)$	None	0	16
2695.1.co	$\chi_{2695}(312, \cdot)$	None	0	16
2695.1.ct	$\chi_{2695}(106, \cdot)$	None	0	24
2695.1.cu	$\chi_{2695}(69, \cdot)$	None	0	24
2695.1.cv	$\chi_{2695}(181, \cdot)$	None	0	24
2695.1.cw	$\chi_{2695}(29, \cdot)$	None	0	24
2695.1.cy	$\chi_{2695}(87, \cdot)$	None	0	24
2695.1.cz	$\chi_{2695}(23, \cdot)$	None	0	24
2695.1.df	$\chi_{2695}(13, \cdot)$	None	0	48
2695.1.dg	$\chi_{2695}(92, \cdot)$	None	0	48
2695.1.di	$\chi_{2695}(26, \cdot)$	None	0	48
2695.1.dj	$\chi_{2695}(39, \cdot)$	None	0	48
2695.1.dk	$\chi_{2695}(46, \cdot)$	None	0	48
2695.1.dl	$\chi_{2695}(59, \cdot)$	None	0	48
2695.1.dq	$\chi_{2695}(37, \cdot)$	None	0	96
2695.1.dr	$\chi_{2695}(17, \cdot)$	None	0	96

Decomposition of $S_{1}^{\mathrm{old}}(\Gamma_1(2695))$ into lower level spaces

$S_{1}^{\mathrm{old}}(\Gamma_1(2695)) \cong$ $S_{1}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(11))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(35))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(49))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(55))$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(77))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(245))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(385))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(539))$$^{\oplus 2}$