Space of modular forms of level 820 and weight 1

• Label: 820.1
• Level: 820
• Weight: 1
• Dimension: 106
• Nonzero newspaces: 9
• Newform subspaces: 19
• Sturm bound: 40320
• Trace bound: 5

Defining parameters

Level:	$N$	=	$820 = 2^{2} \cdot 5 \cdot 41$
Weight:	$k$	=	$1$
Nonzero newspaces:			$9$
Newform subspaces:			$19$
Sturm bound:			$40320$
Trace bound:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(\Gamma_1(820))$.

	Total	New	Old
Modular forms	928	342	586
Cusp forms	128	106	22
Eisenstein series	800	236	564

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	106	0	0	0

Trace form

106 * q - 10 * q^4 - 2 * q^5 - 4 * q^6 - 14 * q^9 - 4 * q^14 + 6 * q^16 - 2 * q^20 - 8 * q^21 - 4 * q^24 - 2 * q^25 - 4 * q^29 + 36 * q^30 - 20 * q^32 - 20 * q^34 + 2 * q^36 - 10 * q^41 + 2 * q^45 - 4 * q^46 - 14 * q^49 + 8 * q^50 - 20 * q^52 + 32 * q^54 - 4 * q^56 - 4 * q^61 - 10 * q^64 - 10 * q^65 - 16 * q^66 - 8 * q^69 - 4 * q^70 - 2 * q^80 - 22 * q^81 - 8 * q^84 - 10 * q^85 - 4 * q^86 - 4 * q^89 + 8 * q^90 - 4 * q^94 - 4 * q^96

Decomposition of $S_{1}^{\mathrm{new}}(\Gamma_1(820))$

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
820.1.c	$\chi_{820}(411, \cdot)$	None	0	1
820.1.e	$\chi_{820}(819, \cdot)$	820.1.e.a	1	1
		820.1.e.b	1
		820.1.e.c	8
820.1.f	$\chi_{820}(739, \cdot)$	None	0	1
820.1.h	$\chi_{820}(491, \cdot)$	None	0	1
820.1.i	$\chi_{820}(173, \cdot)$	None	0	2
820.1.l	$\chi_{820}(573, \cdot)$	None	0	2
820.1.m	$\chi_{820}(91, \cdot)$	None	0	2
820.1.o	$\chi_{820}(319, \cdot)$	820.1.o.a	2	2
		820.1.o.b	2
		820.1.o.c	2
		820.1.o.d	2
820.1.q	$\chi_{820}(493, \cdot)$	None	0	2
820.1.t	$\chi_{820}(73, \cdot)$	None	0	2
820.1.v	$\chi_{820}(161, \cdot)$	None	0	4
820.1.z	$\chi_{820}(167, \cdot)$	820.1.z.a	4	4
820.1.ba	$\chi_{820}(3, \cdot)$	820.1.ba.a	4	4
820.1.bb	$\chi_{820}(109, \cdot)$	None	0	4
820.1.bd	$\chi_{820}(359, \cdot)$	820.1.bd.a	4	4
		820.1.bd.b	4
820.1.bf	$\chi_{820}(51, \cdot)$	None	0	4
820.1.bh	$\chi_{820}(31, \cdot)$	None	0	4
820.1.bj	$\chi_{820}(59, \cdot)$	820.1.bj.a	4	4
		820.1.bj.b	4
820.1.bl	$\chi_{820}(77, \cdot)$	None	0	8
820.1.bn	$\chi_{820}(37, \cdot)$	None	0	8
820.1.bp	$\chi_{820}(39, \cdot)$	820.1.bp.a	8	8
		820.1.bp.b	8
		820.1.bp.c	8
		820.1.bp.d	8
820.1.br	$\chi_{820}(131, \cdot)$	None	0	8
820.1.bs	$\chi_{820}(113, \cdot)$	None	0	8
820.1.bu	$\chi_{820}(33, \cdot)$	None	0	8
820.1.bx	$\chi_{820}(29, \cdot)$	None	0	16
820.1.by	$\chi_{820}(47, \cdot)$	820.1.by.a	16	16
820.1.bz	$\chi_{820}(7, \cdot)$	820.1.bz.a	16	16
820.1.cd	$\chi_{820}(101, \cdot)$	None	0	16

Decomposition of $S_{1}^{\mathrm{old}}(\Gamma_1(820))$ into lower level spaces

$S_{1}^{\mathrm{old}}(\Gamma_1(820)) \cong$ $S_{1}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 12}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(20))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(41))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(82))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(164))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(205))$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(410))$$^{\oplus 2}$