Space of modular forms of level 3060 and weight 2

• Label: 3060.2
• Level: 3060
• Weight: 2
• Dimension: 103798
• Nonzero newspaces: 72
• Sturm bound: 995328
• Trace bound: 70

Defining parameters

Level:	$N$	=	$3060 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 17$
Weight:	$k$	=	$2$
Nonzero newspaces:			$72$
Sturm bound:			$995328$
Trace bound:			$70$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(3060))$.

	Total	New	Old
Modular forms	253952	105414	148538
Cusp forms	243713	103798	139915
Eisenstein series	10239	1616	8623

Trace form

103798 * q - 48 * q^2 - 60 * q^4 - 136 * q^5 - 172 * q^6 - 16 * q^7 - 48 * q^8 - 152 * q^9 - 204 * q^10 - 28 * q^11 - 24 * q^12 - 124 * q^13 + 24 * q^14 - 6 * q^15 - 100 * q^16 - 72 * q^17 - 24 * q^18 - 8 * q^19 + 44 * q^20 - 332 * q^21 + 36 * q^22 + 64 * q^23 + 20 * q^24 - 128 * q^25 - 72 * q^26 + 48 * q^27 - 128 * q^28 + 8 * q^29 - 36 * q^30 - 28 * q^31 - 108 * q^32 + 28 * q^33 - 134 * q^34 + 80 * q^35 - 228 * q^36 - 288 * q^37 - 148 * q^38 + 36 * q^39 - 52 * q^40 - 272 * q^41 - 96 * q^42 - 120 * q^43 - 112 * q^44 - 34 * q^45 - 384 * q^46 - 120 * q^47 + 4 * q^48 - 126 * q^49 - 100 * q^50 - 80 * q^51 - 112 * q^52 - 104 * q^53 + 4 * q^54 - 60 * q^55 - 200 * q^56 - 88 * q^57 + 24 * q^58 - 148 * q^59 - 188 * q^60 - 288 * q^61 - 136 * q^62 - 100 * q^63 - 168 * q^64 - 226 * q^65 - 304 * q^66 - 72 * q^67 - 6 * q^68 - 324 * q^69 - 84 * q^70 - 232 * q^71 - 340 * q^72 - 664 * q^73 - 216 * q^74 - 138 * q^75 + 20 * q^76 - 316 * q^77 - 368 * q^78 - 156 * q^79 - 120 * q^80 - 576 * q^81 + 88 * q^82 - 200 * q^83 - 104 * q^84 - 150 * q^85 + 148 * q^86 - 68 * q^87 + 420 * q^88 - 52 * q^89 - 132 * q^90 + 192 * q^91 + 512 * q^92 + 132 * q^93 + 624 * q^94 - 48 * q^95 + 208 * q^96 + 100 * q^97 + 516 * q^98 + 100 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(3060))$

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
3060.2.a	$\chi_{3060}(1, \cdot)$	3060.2.a.a	1	1
		3060.2.a.b	1
		3060.2.a.c	1
		3060.2.a.d	1
		3060.2.a.e	1
		3060.2.a.f	1
		3060.2.a.g	1
		3060.2.a.h	1
		3060.2.a.i	1
		3060.2.a.j	1
		3060.2.a.k	1
		3060.2.a.l	1
		3060.2.a.m	1
		3060.2.a.n	1
		3060.2.a.o	1
		3060.2.a.p	2
		3060.2.a.q	2
		3060.2.a.r	3
		3060.2.a.s	3
		3060.2.a.t	3
3060.2.b	$\chi_{3060}(3059, \cdot)$	n/a	216	1
3060.2.e	$\chi_{3060}(1801, \cdot)$	3060.2.e.a	2	1
		3060.2.e.b	2
		3060.2.e.c	2
		3060.2.e.d	2
		3060.2.e.e	2
		3060.2.e.f	2
		3060.2.e.g	4
		3060.2.e.h	4
		3060.2.e.i	4
		3060.2.e.j	6
3060.2.g	$\chi_{3060}(2449, \cdot)$	3060.2.g.a	2	1
		3060.2.g.b	2
		3060.2.g.c	2
		3060.2.g.d	2
		3060.2.g.e	2
		3060.2.g.f	8
		3060.2.g.g	10
		3060.2.g.h	12
3060.2.h	$\chi_{3060}(1871, \cdot)$	n/a	128	1
3060.2.k	$\chi_{3060}(1189, \cdot)$	3060.2.k.a	2	1
		3060.2.k.b	2
		3060.2.k.c	4
		3060.2.k.d	4
		3060.2.k.e	4
		3060.2.k.f	4
		3060.2.k.g	8
		3060.2.k.h	8
		3060.2.k.i	8
3060.2.l	$\chi_{3060}(611, \cdot)$	n/a	144	1
3060.2.n	$\chi_{3060}(1259, \cdot)$	n/a	192	1
3060.2.q	$\chi_{3060}(1021, \cdot)$	n/a	128	2
3060.2.s	$\chi_{3060}(1747, \cdot)$	n/a	532	2
3060.2.t	$\chi_{3060}(2393, \cdot)$	3060.2.t.a	72	2
3060.2.w	$\chi_{3060}(953, \cdot)$	3060.2.w.a	4	2
		3060.2.w.b	4
		3060.2.w.c	8
		3060.2.w.d	8
		3060.2.w.e	12
		3060.2.w.f	28
3060.2.x	$\chi_{3060}(307, \cdot)$	n/a	480	2
3060.2.z	$\chi_{3060}(829, \cdot)$	3060.2.z.a	2	2
		3060.2.z.b	2
		3060.2.z.c	4
		3060.2.z.d	4
		3060.2.z.e	12
		3060.2.z.f	24
		3060.2.z.g	40
3060.2.bb	$\chi_{3060}(1619, \cdot)$	n/a	432	2
3060.2.be	$\chi_{3060}(361, \cdot)$	3060.2.be.a	12	2
		3060.2.be.b	12
		3060.2.be.c	12
		3060.2.be.d	24
3060.2.bg	$\chi_{3060}(251, \cdot)$	n/a	288	2
3060.2.bh	$\chi_{3060}(917, \cdot)$	3060.2.bh.a	24	2
		3060.2.bh.b	48
3060.2.bk	$\chi_{3060}(883, \cdot)$	n/a	532	2
3060.2.bl	$\chi_{3060}(523, \cdot)$	n/a	532	2
3060.2.bo	$\chi_{3060}(557, \cdot)$	3060.2.bo.a	72	2
3060.2.bq	$\chi_{3060}(239, \cdot)$	n/a	1152	2
3060.2.bs	$\chi_{3060}(1631, \cdot)$	n/a	864	2
3060.2.bv	$\chi_{3060}(169, \cdot)$	n/a	216	2
3060.2.bw	$\chi_{3060}(851, \cdot)$	n/a	768	2
3060.2.bz	$\chi_{3060}(409, \cdot)$	n/a	192	2
3060.2.cb	$\chi_{3060}(781, \cdot)$	n/a	144	2
3060.2.cc	$\chi_{3060}(1019, \cdot)$	n/a	1280	2
3060.2.ce	$\chi_{3060}(791, \cdot)$	n/a	576	4
3060.2.cf	$\chi_{3060}(1981, \cdot)$	n/a	120	4
3060.2.ci	$\chi_{3060}(773, \cdot)$	n/a	144	4
3060.2.cj	$\chi_{3060}(127, \cdot)$	n/a	1064	4
3060.2.co	$\chi_{3060}(1063, \cdot)$	n/a	1064	4
3060.2.cp	$\chi_{3060}(53, \cdot)$	n/a	144	4
3060.2.cs	$\chi_{3060}(1369, \cdot)$	n/a	184	4
3060.2.ct	$\chi_{3060}(179, \cdot)$	n/a	864	4
3060.2.cv	$\chi_{3060}(1543, \cdot)$	n/a	2560	4
3060.2.cw	$\chi_{3060}(293, \cdot)$	n/a	432	4
3060.2.cz	$\chi_{3060}(713, \cdot)$	n/a	432	4
3060.2.da	$\chi_{3060}(67, \cdot)$	n/a	2560	4
3060.2.dc	$\chi_{3060}(421, \cdot)$	n/a	288	4
3060.2.de	$\chi_{3060}(191, \cdot)$	n/a	1728	4
3060.2.dh	$\chi_{3060}(769, \cdot)$	n/a	432	4
3060.2.dj	$\chi_{3060}(599, \cdot)$	n/a	2560	4
3060.2.dk	$\chi_{3060}(137, \cdot)$	n/a	384	4
3060.2.dn	$\chi_{3060}(103, \cdot)$	n/a	2304	4
3060.2.do	$\chi_{3060}(463, \cdot)$	n/a	2560	4
3060.2.dr	$\chi_{3060}(353, \cdot)$	n/a	432	4
3060.2.du	$\chi_{3060}(73, \cdot)$	n/a	360	8
3060.2.dv	$\chi_{3060}(683, \cdot)$	n/a	1728	8
3060.2.dw	$\chi_{3060}(199, \cdot)$	n/a	2128	8
3060.2.dy	$\chi_{3060}(521, \cdot)$	n/a	192	8
3060.2.eb	$\chi_{3060}(91, \cdot)$	n/a	1440	8
3060.2.ed	$\chi_{3060}(269, \cdot)$	n/a	288	8
3060.2.ee	$\chi_{3060}(37, \cdot)$	n/a	360	8
3060.2.ef	$\chi_{3060}(107, \cdot)$	n/a	1728	8
3060.2.ei	$\chi_{3060}(59, \cdot)$	n/a	5120	8
3060.2.ej	$\chi_{3060}(49, \cdot)$	n/a	864	8
3060.2.eo	$\chi_{3060}(77, \cdot)$	n/a	864	8
3060.2.ep	$\chi_{3060}(43, \cdot)$	n/a	5120	8
3060.2.eq	$\chi_{3060}(223, \cdot)$	n/a	5120	8
3060.2.er	$\chi_{3060}(257, \cdot)$	n/a	864	8
3060.2.ew	$\chi_{3060}(121, \cdot)$	n/a	576	8
3060.2.ex	$\chi_{3060}(491, \cdot)$	n/a	3456	8
3060.2.fa	$\chi_{3060}(23, \cdot)$	n/a	10240	16
3060.2.fb	$\chi_{3060}(97, \cdot)$	n/a	1728	16
3060.2.fc	$\chi_{3060}(29, \cdot)$	n/a	1728	16
3060.2.fe	$\chi_{3060}(31, \cdot)$	n/a	6912	16
3060.2.fh	$\chi_{3060}(41, \cdot)$	n/a	1152	16
3060.2.fj	$\chi_{3060}(79, \cdot)$	n/a	10240	16
3060.2.fk	$\chi_{3060}(227, \cdot)$	n/a	10240	16
3060.2.fl	$\chi_{3060}(133, \cdot)$	n/a	1728	16

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(3060))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(3060)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 36}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 24}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(12))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(36))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(153))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(170))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(180))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(204))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(255))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(306))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(340))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(510))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(612))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(765))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1020))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1530))$$^{\oplus 2}$