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

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