Space of modular forms of level 3328 and weight 2

• Label: 3328.2
• Level: 3328
• Weight: 2
• Dimension: 190088
• Nonzero newspaces: 44
• Sturm bound: 1376256
• Trace bound: 52

Defining parameters

Level:	$N$	=	$3328 = 2^{8} \cdot 13$
Weight:	$k$	=	$2$
Nonzero newspaces:			$44$
Sturm bound:			$1376256$
Trace bound:			$52$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(3328))$.

	Total	New	Old
Modular forms	348288	192376	155912
Cusp forms	339841	190088	149753
Eisenstein series	8447	2288	6159

Trace form

190088 * q - 320 * q^2 - 240 * q^3 - 320 * q^4 - 320 * q^5 - 320 * q^6 - 240 * q^7 - 320 * q^8 - 400 * q^9 - 320 * q^10 - 240 * q^11 - 320 * q^12 - 352 * q^13 - 704 * q^14 - 240 * q^15 - 320 * q^16 - 480 * q^17 - 320 * q^18 - 240 * q^19 - 320 * q^20 - 320 * q^21 - 320 * q^22 - 240 * q^23 - 320 * q^24 - 400 * q^25 - 352 * q^26 - 528 * q^27 - 320 * q^28 - 320 * q^29 - 320 * q^30 - 224 * q^31 - 320 * q^32 - 560 * q^33 - 320 * q^34 - 240 * q^35 - 320 * q^36 - 320 * q^37 - 320 * q^38 - 264 * q^39 - 704 * q^40 - 400 * q^41 - 320 * q^42 - 240 * q^43 - 320 * q^44 - 272 * q^45 - 320 * q^46 - 240 * q^47 - 320 * q^48 - 424 * q^49 - 320 * q^50 - 176 * q^51 - 352 * q^52 - 640 * q^53 - 320 * q^54 - 112 * q^55 - 320 * q^56 - 272 * q^57 - 320 * q^58 - 112 * q^59 - 320 * q^60 - 192 * q^61 - 320 * q^62 - 96 * q^63 - 320 * q^64 - 728 * q^65 - 704 * q^66 - 80 * q^67 - 320 * q^68 - 192 * q^69 - 320 * q^70 - 112 * q^71 - 320 * q^72 - 272 * q^73 - 320 * q^74 - 112 * q^75 - 320 * q^76 - 256 * q^77 - 352 * q^78 - 464 * q^79 - 320 * q^80 - 408 * q^81 - 320 * q^82 - 240 * q^83 - 320 * q^84 - 240 * q^85 - 320 * q^86 - 240 * q^87 - 320 * q^88 - 400 * q^89 - 320 * q^90 - 264 * q^91 - 704 * q^92 - 416 * q^93 - 320 * q^94 - 224 * q^95 - 320 * q^96 - 560 * q^97 - 320 * q^98 - 192 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(3328))$

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
3328.2.a	$\chi_{3328}(1, \cdot)$	3328.2.a.a	1	1
		3328.2.a.b	1
		3328.2.a.c	1
		3328.2.a.d	1
		3328.2.a.e	1
		3328.2.a.f	1
		3328.2.a.g	1
		3328.2.a.h	1
		3328.2.a.i	1
		3328.2.a.j	1
		3328.2.a.k	1
		3328.2.a.l	1
		3328.2.a.m	2
		3328.2.a.n	2
		3328.2.a.o	2
		3328.2.a.p	2
		3328.2.a.q	2
		3328.2.a.r	2
		3328.2.a.s	2
		3328.2.a.t	2
		3328.2.a.u	2
		3328.2.a.v	2
		3328.2.a.w	2
		3328.2.a.x	2
		3328.2.a.y	2
		3328.2.a.z	2
		3328.2.a.ba	2
		3328.2.a.bb	2
		3328.2.a.bc	2
		3328.2.a.bd	2
		3328.2.a.be	3
		3328.2.a.bf	3
		3328.2.a.bg	3
		3328.2.a.bh	3
		3328.2.a.bi	4
		3328.2.a.bj	4
		3328.2.a.bk	4
		3328.2.a.bl	4
		3328.2.a.bm	4
		3328.2.a.bn	4
		3328.2.a.bo	6
		3328.2.a.bp	6
3328.2.b	$\chi_{3328}(1665, \cdot)$	3328.2.b.a	2	1
		3328.2.b.b	2
		3328.2.b.c	2
		3328.2.b.d	2
		3328.2.b.e	2
		3328.2.b.f	2
		3328.2.b.g	2
		3328.2.b.h	2
		3328.2.b.i	2
		3328.2.b.j	2
		3328.2.b.k	2
		3328.2.b.l	2
		3328.2.b.m	2
		3328.2.b.n	2
		3328.2.b.o	2
		3328.2.b.p	2
		3328.2.b.q	2
		3328.2.b.r	2
		3328.2.b.s	2
		3328.2.b.t	2
		3328.2.b.u	4
		3328.2.b.v	4
		3328.2.b.w	4
		3328.2.b.x	4
		3328.2.b.y	4
		3328.2.b.z	4
		3328.2.b.ba	4
		3328.2.b.bb	8
		3328.2.b.bc	10
		3328.2.b.bd	10
3328.2.e	$\chi_{3328}(129, \cdot)$	n/a	108	1
3328.2.f	$\chi_{3328}(1793, \cdot)$	n/a	108	1
3328.2.i	$\chi_{3328}(1537, \cdot)$	n/a	216	2
3328.2.k	$\chi_{3328}(255, \cdot)$	n/a	216	2
3328.2.l	$\chi_{3328}(447, \cdot)$	n/a	224	2
3328.2.n	$\chi_{3328}(833, \cdot)$	n/a	192	2
3328.2.p	$\chi_{3328}(961, \cdot)$	n/a	224	2
3328.2.s	$\chi_{3328}(2111, \cdot)$	n/a	224	2
3328.2.u	$\chi_{3328}(1919, \cdot)$	n/a	216	2
3328.2.w	$\chi_{3328}(257, \cdot)$	n/a	216	2
3328.2.z	$\chi_{3328}(1153, \cdot)$	n/a	216	2
3328.2.ba	$\chi_{3328}(641, \cdot)$	n/a	216	2
3328.2.bd	$\chi_{3328}(671, \cdot)$	n/a	432	4
3328.2.bf	$\chi_{3328}(417, \cdot)$	n/a	384	4
3328.2.bg	$\chi_{3328}(545, \cdot)$	n/a	432	4
3328.2.bi	$\chi_{3328}(31, \cdot)$	n/a	432	4
3328.2.bk	$\chi_{3328}(383, \cdot)$	n/a	432	4
3328.2.bn	$\chi_{3328}(63, \cdot)$	n/a	448	4
3328.2.bp	$\chi_{3328}(1089, \cdot)$	n/a	448	4
3328.2.br	$\chi_{3328}(321, \cdot)$	n/a	448	4
3328.2.bs	$\chi_{3328}(1727, \cdot)$	n/a	448	4
3328.2.bu	$\chi_{3328}(2047, \cdot)$	n/a	432	4
3328.2.bw	$\chi_{3328}(47, \cdot)$	n/a	880	8
3328.2.by	$\chi_{3328}(209, \cdot)$	n/a	768	8
3328.2.cb	$\chi_{3328}(337, \cdot)$	n/a	880	8
3328.2.cc	$\chi_{3328}(239, \cdot)$	n/a	880	8
3328.2.cf	$\chi_{3328}(479, \cdot)$	n/a	864	8
3328.2.ch	$\chi_{3328}(225, \cdot)$	n/a	864	8
3328.2.ci	$\chi_{3328}(289, \cdot)$	n/a	864	8
3328.2.ck	$\chi_{3328}(223, \cdot)$	n/a	864	8
3328.2.cn	$\chi_{3328}(135, \cdot)$	None	0	16
3328.2.cp	$\chi_{3328}(105, \cdot)$	None	0	16
3328.2.cr	$\chi_{3328}(25, \cdot)$	None	0	16
3328.2.cs	$\chi_{3328}(343, \cdot)$	None	0	16
3328.2.cv	$\chi_{3328}(175, \cdot)$	n/a	1760	16
3328.2.cx	$\chi_{3328}(81, \cdot)$	n/a	1760	16
3328.2.cy	$\chi_{3328}(17, \cdot)$	n/a	1760	16
3328.2.db	$\chi_{3328}(15, \cdot)$	n/a	1760	16
3328.2.dc	$\chi_{3328}(83, \cdot)$	n/a	14272	32
3328.2.de	$\chi_{3328}(77, \cdot)$	n/a	14272	32
3328.2.df	$\chi_{3328}(53, \cdot)$	n/a	12288	32
3328.2.di	$\chi_{3328}(99, \cdot)$	n/a	14272	32
3328.2.dk	$\chi_{3328}(71, \cdot)$	None	0	32
3328.2.dm	$\chi_{3328}(121, \cdot)$	None	0	32
3328.2.do	$\chi_{3328}(9, \cdot)$	None	0	32
3328.2.dr	$\chi_{3328}(7, \cdot)$	None	0	32
3328.2.dt	$\chi_{3328}(115, \cdot)$	n/a	28544	64
3328.2.dw	$\chi_{3328}(69, \cdot)$	n/a	28544	64
3328.2.dx	$\chi_{3328}(29, \cdot)$	n/a	28544	64
3328.2.dz	$\chi_{3328}(11, \cdot)$	n/a	28544	64

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(3328))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(3328)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 18}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 14}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$^{\oplus 7}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(128))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(256))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(416))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(832))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(1664))$$^{\oplus 2}$