Space of modular forms of level 3362 and weight 2

• Label: 3362.2
• Level: 3362
• Weight: 2
• Dimension: 117531
• Nonzero newspaces: 12
• Sturm bound: 1412040
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 3362 = 2 \cdot 41^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(1412040\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3362))\).

	Total	New	Old
Modular forms	355450	117531	237919
Cusp forms	350571	117531	233040
Eisenstein series	4879	0	4879

Trace form

117531 * q + q^2 + 4 * q^3 + q^4 + 6 * q^5 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 + 6 * q^10 + 12 * q^11 + 4 * q^12 + 14 * q^13 + 8 * q^14 + 24 * q^15 + q^16 + 18 * q^17 + 13 * q^18 + 20 * q^19 + 6 * q^20 + 32 * q^21 + 12 * q^22 + 24 * q^23 + 4 * q^24 + 31 * q^25 + 14 * q^26 + 40 * q^27 + 8 * q^28 + 30 * q^29 - 56 * q^30 - 48 * q^31 - 19 * q^32 - 192 * q^33 - 82 * q^34 - 112 * q^35 - 27 * q^36 - 202 * q^37 - 60 * q^38 - 264 * q^39 - 74 * q^40 - 40 * q^41 - 288 * q^42 - 36 * q^43 - 68 * q^44 - 242 * q^45 - 56 * q^46 - 192 * q^47 - 36 * q^48 - 103 * q^49 - 69 * q^50 - 168 * q^51 - 6 * q^52 - 26 * q^53 - 40 * q^54 + 72 * q^55 + 8 * q^56 + 80 * q^57 + 30 * q^58 + 60 * q^59 + 24 * q^60 + 62 * q^61 + 32 * q^62 + 104 * q^63 + q^64 + 64 * q^65 + 48 * q^66 - 52 * q^67 + 18 * q^68 - 64 * q^69 + 48 * q^70 - 88 * q^71 + 13 * q^72 - 86 * q^73 + 38 * q^74 - 196 * q^75 + 20 * q^76 - 64 * q^77 + 56 * q^78 - 80 * q^79 + 6 * q^80 - 219 * q^81 - 76 * q^83 + 32 * q^84 - 232 * q^85 + 44 * q^86 - 40 * q^87 + 12 * q^88 - 70 * q^89 + 78 * q^90 - 208 * q^91 + 24 * q^92 - 32 * q^93 + 48 * q^94 - 40 * q^95 + 4 * q^96 - 62 * q^97 + 57 * q^98 + 36 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3362))\)

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
3362.2.a	\(\chi_{3362}(1, \cdot)\)	3362.2.a.a	1	1
		3362.2.a.b	1
		3362.2.a.c	1
		3362.2.a.d	2
		3362.2.a.e	2
		3362.2.a.f	2
		3362.2.a.g	2
		3362.2.a.h	2
		3362.2.a.i	2
		3362.2.a.j	2
		3362.2.a.k	2
		3362.2.a.l	2
		3362.2.a.m	2
		3362.2.a.n	2
		3362.2.a.o	2
		3362.2.a.p	2
		3362.2.a.q	3
		3362.2.a.r	3
		3362.2.a.s	3
		3362.2.a.t	3
		3362.2.a.u	4
		3362.2.a.v	4
		3362.2.a.w	8
		3362.2.a.x	8
		3362.2.a.y	8
		3362.2.a.z	12
		3362.2.a.ba	12
		3362.2.a.bb	12
		3362.2.a.bc	12
		3362.2.a.bd	16
3362.2.b	\(\chi_{3362}(3361, \cdot)\)	n/a	136	1
3362.2.c	\(\chi_{3362}(1303, \cdot)\)	n/a	274	2
3362.2.d	\(\chi_{3362}(51, \cdot)\)	n/a	544	4
3362.2.f	\(\chi_{3362}(761, \cdot)\)	n/a	544	4
3362.2.g	\(\chi_{3362}(207, \cdot)\)	n/a	1096	8
3362.2.i	\(\chi_{3362}(83, \cdot)\)	n/a	5760	40
3362.2.j	\(\chi_{3362}(81, \cdot)\)	n/a	5760	40
3362.2.k	\(\chi_{3362}(9, \cdot)\)	n/a	11440	80
3362.2.l	\(\chi_{3362}(37, \cdot)\)	n/a	23040	160
3362.2.n	\(\chi_{3362}(23, \cdot)\)	n/a	23040	160
3362.2.o	\(\chi_{3362}(5, \cdot)\)	n/a	45760	320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3362))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3362)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1681))\)\(^{\oplus 2}\)