Space of modular forms of level 1859 and weight 4

• Label: 1859.4
• Level: 1859
• Weight: 4
• Dimension: 412000
• Nonzero newspaces: 24
• Sturm bound: 1135680
• Trace bound: 3

Defining parameters

Level:	$N$	=	$1859 = 11 \cdot 13^{2}$
Weight:	$k$	=	$4$
Nonzero newspaces:			$24$
Sturm bound:			$1135680$
Trace bound:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(\Gamma_1(1859))$.

	Total	New	Old
Modular forms	428160	415680	12480
Cusp forms	423600	412000	11600
Eisenstein series	4560	3680	880

Trace form

412000 * q - 533 * q^2 - 533 * q^3 - 533 * q^4 - 533 * q^5 - 583 * q^6 - 687 * q^7 - 781 * q^8 - 453 * q^9 - 78 * q^10 - 429 * q^11 - 102 * q^12 - 288 * q^13 - 728 * q^14 - 555 * q^15 - 913 * q^16 - 1439 * q^17 - 3850 * q^18 - 2084 * q^19 - 2162 * q^20 - 118 * q^21 + 811 * q^22 - 386 * q^23 + 3501 * q^24 + 883 * q^25 + 924 * q^26 + 2194 * q^27 - 914 * q^28 - 2299 * q^29 - 3212 * q^30 - 2171 * q^31 - 2924 * q^32 - 2004 * q^33 - 4322 * q^34 - 463 * q^35 - 1112 * q^36 + 339 * q^37 + 5300 * q^38 - 432 * q^39 - 1832 * q^40 - 1907 * q^41 - 3018 * q^42 - 2918 * q^43 - 1246 * q^44 + 832 * q^45 + 3674 * q^46 + 585 * q^47 - 644 * q^48 + 4345 * q^49 - 827 * q^50 - 2498 * q^51 - 1236 * q^52 + 799 * q^53 - 834 * q^54 + 609 * q^55 + 1380 * q^56 + 2718 * q^57 + 4776 * q^58 + 2750 * q^59 + 5804 * q^60 - 4737 * q^61 - 8402 * q^62 - 13068 * q^63 - 18577 * q^64 - 8694 * q^65 - 8114 * q^66 - 3996 * q^67 + 6126 * q^68 + 8504 * q^69 + 7556 * q^70 + 7713 * q^71 + 11431 * q^72 + 5557 * q^73 + 8298 * q^74 + 1264 * q^75 - 7682 * q^76 - 2073 * q^77 + 4596 * q^78 - 5393 * q^79 + 9572 * q^80 + 10719 * q^82 + 13720 * q^83 + 7748 * q^84 + 6375 * q^85 - 10831 * q^86 - 12618 * q^87 + 3205 * q^88 - 14128 * q^89 - 28398 * q^90 - 6024 * q^91 - 22698 * q^92 - 19995 * q^93 - 7682 * q^94 - 6717 * q^95 + 5988 * q^96 + 7570 * q^97 - 9554 * q^98 + 11413 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(\Gamma_1(1859))$

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
1859.4.a	$\chi_{1859}(1, \cdot)$	1859.4.a.a	2	1
		1859.4.a.b	4
		1859.4.a.c	6
		1859.4.a.d	9
		1859.4.a.e	11
		1859.4.a.f	17
		1859.4.a.g	17
		1859.4.a.h	17
		1859.4.a.i	17
		1859.4.a.j	18
		1859.4.a.k	18
		1859.4.a.l	36
		1859.4.a.m	36
		1859.4.a.n	39
		1859.4.a.o	39
		1859.4.a.p	51
		1859.4.a.q	51
1859.4.b	$\chi_{1859}(1013, \cdot)$	n/a	384	1
1859.4.e	$\chi_{1859}(529, \cdot)$	n/a	772	2
1859.4.g	$\chi_{1859}(1253, \cdot)$	n/a	904	2
1859.4.h	$\chi_{1859}(170, \cdot)$	n/a	1816	4
1859.4.j	$\chi_{1859}(23, \cdot)$	n/a	768	2
1859.4.n	$\chi_{1859}(168, \cdot)$	n/a	1808	4
1859.4.o	$\chi_{1859}(934, \cdot)$	n/a	1808	4
1859.4.q	$\chi_{1859}(144, \cdot)$	n/a	5448	12
1859.4.r	$\chi_{1859}(146, \cdot)$	n/a	3616	8
1859.4.t	$\chi_{1859}(239, \cdot)$	n/a	3616	8
1859.4.w	$\chi_{1859}(12, \cdot)$	n/a	5472	12
1859.4.y	$\chi_{1859}(147, \cdot)$	n/a	3616	8
1859.4.ba	$\chi_{1859}(100, \cdot)$	n/a	10896	24
1859.4.bb	$\chi_{1859}(21, \cdot)$	n/a	13056	24
1859.4.bd	$\chi_{1859}(19, \cdot)$	n/a	7232	16
1859.4.bf	$\chi_{1859}(14, \cdot)$	n/a	26112	48
1859.4.bh	$\chi_{1859}(56, \cdot)$	n/a	10944	24
1859.4.bj	$\chi_{1859}(25, \cdot)$	n/a	26112	48
1859.4.bn	$\chi_{1859}(32, \cdot)$	n/a	26112	48
1859.4.bo	$\chi_{1859}(3, \cdot)$	n/a	52224	96
1859.4.bp	$\chi_{1859}(8, \cdot)$	n/a	52224	96
1859.4.bs	$\chi_{1859}(4, \cdot)$	n/a	52224	96
1859.4.bv	$\chi_{1859}(2, \cdot)$	n/a	104448	192

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

Decomposition of $S_{4}^{\mathrm{old}}(\Gamma_1(1859))$ into lower level spaces

$S_{4}^{\mathrm{old}}(\Gamma_1(1859)) \cong$ $S_{4}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_1(143))$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(\Gamma_1(169))$$^{\oplus 2}$