Space of modular forms of level 2738 and weight 2

• Label: 2738.2
• Level: 2738
• Weight: 2
• Dimension: 77920
• Nonzero newspaces: 12
• Sturm bound: 936396
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(936396\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2738))\).

	Total	New	Old
Modular forms	236079	77920	158159
Cusp forms	232120	77920	154200
Eisenstein series	3959	0	3959

Trace form

77920 * 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 - 4 * q^26 - 56 * q^27 - 16 * q^28 - 42 * q^29 - 120 * q^30 - 184 * q^31 + q^32 - 96 * q^33 - 126 * q^34 - 168 * q^35 - 77 * q^36 - 84 * q^37 - 52 * q^38 - 112 * q^39 - 84 * q^40 - 174 * q^41 - 112 * q^42 - 100 * q^43 + 12 * q^44 - 138 * q^45 - 120 * q^46 - 24 * q^47 - 20 * q^48 - 39 * q^49 + 13 * q^50 + 72 * q^51 + 14 * q^52 + 54 * q^53 + 40 * q^54 + 72 * q^55 + 8 * q^56 + 80 * q^57 + 30 * q^58 - 12 * q^59 + 24 * q^60 - 28 * q^61 + 32 * q^62 - 112 * q^63 + q^64 - 78 * q^65 + 48 * q^66 - 4 * q^67 + 18 * q^68 - 192 * q^69 + 48 * q^70 - 72 * q^71 + 13 * q^72 - 70 * q^73 - 236 * q^75 + 20 * q^76 - 48 * q^77 + 56 * q^78 - 64 * q^79 + 6 * q^80 - 167 * q^81 + 42 * q^82 + 12 * q^83 + 32 * q^84 - 54 * q^85 + 44 * q^86 - 96 * q^87 + 12 * q^88 + 78 * q^90 + 16 * q^91 - 48 * q^92 - 88 * q^93 - 96 * q^94 - 168 * q^95 + 4 * q^96 - 190 * q^97 - 231 * q^98 - 204 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2738))\)

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
2738.2.a	\(\chi_{2738}(1, \cdot)\)	2738.2.a.a	1	1
		2738.2.a.b	1
		2738.2.a.c	1
		2738.2.a.d	1
		2738.2.a.e	2
		2738.2.a.f	2
		2738.2.a.g	2
		2738.2.a.h	2
		2738.2.a.i	2
		2738.2.a.j	2
		2738.2.a.k	2
		2738.2.a.l	2
		2738.2.a.m	3
		2738.2.a.n	3
		2738.2.a.o	3
		2738.2.a.p	3
		2738.2.a.q	6
		2738.2.a.r	6
		2738.2.a.s	6
		2738.2.a.t	6
		2738.2.a.u	9
		2738.2.a.v	9
		2738.2.a.w	18
		2738.2.a.x	18
2738.2.b	\(\chi_{2738}(2737, \cdot)\)	n/a	110	1
2738.2.c	\(\chi_{2738}(581, \cdot)\)	n/a	218	2
2738.2.e	\(\chi_{2738}(1951, \cdot)\)	n/a	220	2
2738.2.f	\(\chi_{2738}(737, \cdot)\)	n/a	666	6
2738.2.h	\(\chi_{2738}(437, \cdot)\)	n/a	672	6
2738.2.j	\(\chi_{2738}(75, \cdot)\)	n/a	4284	36
2738.2.k	\(\chi_{2738}(73, \cdot)\)	n/a	4248	36
2738.2.l	\(\chi_{2738}(47, \cdot)\)	n/a	8568	72
2738.2.n	\(\chi_{2738}(11, \cdot)\)	n/a	8496	72
2738.2.o	\(\chi_{2738}(7, \cdot)\)	n/a	25272	216
2738.2.q	\(\chi_{2738}(3, \cdot)\)	n/a	25056	216

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2738))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2738)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1369))\)\(^{\oplus 2}\)