Space of modular forms of level 1338 and weight 2

• Label: 1338.2
• Level: 1338
• Weight: 2
• Dimension: 12433
• Nonzero newspaces: 8
• Sturm bound: 198912
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(198912\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1338))\).

	Total	New	Old
Modular forms	50616	12433	38183
Cusp forms	48841	12433	36408
Eisenstein series	1775	0	1775

Trace form

12433 * q + q^2 + q^3 + q^4 + 6 * q^5 + q^6 + 8 * q^7 + q^8 + q^9 + 6 * q^10 + 12 * q^11 + q^12 + 14 * q^13 + 8 * q^14 + 6 * q^15 + q^16 + 18 * q^17 + q^18 + 20 * q^19 + 6 * q^20 + 8 * q^21 + 12 * q^22 + 24 * q^23 + q^24 + 31 * q^25 + 14 * q^26 + q^27 + 8 * q^28 + 30 * q^29 + 6 * q^30 + 32 * q^31 + q^32 + 12 * q^33 + 18 * q^34 + 48 * q^35 + q^36 + 38 * q^37 + 20 * q^38 + 14 * q^39 + 6 * q^40 + 42 * q^41 + 8 * q^42 + 44 * q^43 + 12 * q^44 + 6 * q^45 + 24 * q^46 + 48 * q^47 + q^48 + 57 * q^49 + 31 * q^50 + 18 * q^51 + 14 * q^52 + 54 * q^53 + q^54 + 72 * q^55 + 8 * q^56 + 20 * q^57 + 30 * q^58 + 60 * q^59 + 6 * q^60 + 62 * q^61 + 32 * q^62 + 8 * q^63 + q^64 + 84 * q^65 + 12 * q^66 + 68 * q^67 + 18 * q^68 + 24 * q^69 + 48 * q^70 + 72 * q^71 + q^72 + 74 * q^73 + 38 * q^74 + 31 * q^75 + 20 * q^76 + 96 * q^77 + 14 * q^78 + 80 * q^79 + 6 * q^80 + q^81 + 42 * q^82 + 84 * q^83 + 8 * q^84 + 108 * q^85 + 44 * q^86 + 30 * q^87 + 12 * q^88 + 90 * q^89 + 6 * q^90 + 112 * q^91 + 24 * q^92 + 32 * q^93 + 48 * q^94 + 120 * q^95 + q^96 + 98 * q^97 + 57 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1338))\)

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
1338.2.a	\(\chi_{1338}(1, \cdot)\)	1338.2.a.a	1	1
		1338.2.a.b	2
		1338.2.a.c	3
		1338.2.a.d	3
		1338.2.a.e	3
		1338.2.a.f	3
		1338.2.a.g	4
		1338.2.a.h	5
		1338.2.a.i	6
		1338.2.a.j	7
1338.2.d	\(\chi_{1338}(1337, \cdot)\)	1338.2.d.a	76	1
1338.2.e	\(\chi_{1338}(931, \cdot)\)	1338.2.e.a	2	2
		1338.2.e.b	2
		1338.2.e.c	2
		1338.2.e.d	4
		1338.2.e.e	4
		1338.2.e.f	4
		1338.2.e.g	12
		1338.2.e.h	14
		1338.2.e.i	14
		1338.2.e.j	18
1338.2.f	\(\chi_{1338}(263, \cdot)\)	n/a	148	2
1338.2.i	\(\chi_{1338}(7, \cdot)\)	n/a	1296	36
1338.2.j	\(\chi_{1338}(59, \cdot)\)	n/a	2736	36
1338.2.m	\(\chi_{1338}(19, \cdot)\)	n/a	2736	72
1338.2.p	\(\chi_{1338}(5, \cdot)\)	n/a	5328	72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1338))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1338)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(446))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 2}\)