Space of modular forms of level 238 and weight 2

• Label: 238.2
• Level: 238
• Weight: 2
• Dimension: 551
• Nonzero newspaces: 10
• Newform subspaces: 32
• Sturm bound: 6912
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 238 = 2 \cdot 7 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(6912\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(238))\).

	Total	New	Old
Modular forms	1920	551	1369
Cusp forms	1537	551	986
Eisenstein series	383	0	383

Trace form

551 * q + 3 * q^2 + 8 * q^3 - q^4 + 6 * q^5 - q^7 + 3 * q^8 + 11 * q^9 - 2 * q^10 - 20 * q^11 - 8 * q^12 - 10 * q^13 - 13 * q^14 - 72 * q^15 - 9 * q^16 - 21 * q^17 - 49 * q^18 - 16 * q^19 - 2 * q^20 - 40 * q^21 - 20 * q^22 - 8 * q^23 - 16 * q^24 - 31 * q^25 - 2 * q^26 - 16 * q^27 - q^28 + 2 * q^29 + 24 * q^30 - 24 * q^31 + 3 * q^32 - 16 * q^33 + 23 * q^34 - 26 * q^35 + 11 * q^36 - 30 * q^37 + 8 * q^38 - 88 * q^39 + 6 * q^40 - 106 * q^41 - 48 * q^42 - 84 * q^43 - 52 * q^44 - 90 * q^45 - 40 * q^46 - 88 * q^47 + 8 * q^48 - 65 * q^49 - 91 * q^50 - 48 * q^51 - 42 * q^52 - 94 * q^53 - 64 * q^54 - 88 * q^55 + 3 * q^56 - 88 * q^57 - 46 * q^58 - 88 * q^59 - 40 * q^60 - 50 * q^61 - 72 * q^62 - 85 * q^63 - q^64 + 12 * q^65 + 32 * q^66 + 44 * q^67 + 3 * q^68 - 32 * q^69 - 26 * q^70 - 24 * q^71 - 25 * q^72 - 98 * q^73 - 30 * q^74 - 120 * q^75 + 16 * q^76 - 68 * q^77 - 56 * q^78 - 96 * q^79 - 26 * q^80 - 65 * q^81 - 82 * q^82 - 48 * q^83 - 24 * q^84 - 162 * q^85 - 4 * q^86 - 192 * q^87 - 52 * q^88 - 90 * q^89 - 58 * q^90 - 138 * q^91 - 8 * q^92 - 144 * q^93 - 104 * q^94 - 168 * q^95 - 74 * q^97 - 5 * q^98 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)

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
238.2.a	\(\chi_{238}(1, \cdot)\)	238.2.a.a	1	1
		238.2.a.b	1
		238.2.a.c	1
		238.2.a.d	1
		238.2.a.e	1
		238.2.a.f	2
238.2.b	\(\chi_{238}(169, \cdot)\)	238.2.b.a	2	1
		238.2.b.b	6
238.2.e	\(\chi_{238}(137, \cdot)\)	238.2.e.a	2	2
		238.2.e.b	2
		238.2.e.c	2
		238.2.e.d	2
		238.2.e.e	6
		238.2.e.f	10
238.2.g	\(\chi_{238}(183, \cdot)\)	238.2.g.a	8	2
		238.2.g.b	8
238.2.j	\(\chi_{238}(67, \cdot)\)	238.2.j.a	4	2
		238.2.j.b	8
		238.2.j.c	12
238.2.k	\(\chi_{238}(15, \cdot)\)	238.2.k.a	16	4
		238.2.k.b	24
238.2.n	\(\chi_{238}(81, \cdot)\)	238.2.n.a	4	4
		238.2.n.b	4
		238.2.n.c	16
		238.2.n.d	24
238.2.p	\(\chi_{238}(27, \cdot)\)	238.2.p.a	48	8
		238.2.p.b	48
238.2.q	\(\chi_{238}(9, \cdot)\)	238.2.q.a	16	8
		238.2.q.b	32
		238.2.q.c	48
238.2.s	\(\chi_{238}(3, \cdot)\)	238.2.s.a	96	16
		238.2.s.b	96

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(238))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(238)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)