Space of modular forms of level 234 and weight 2

• Label: 234.2
• Level: 234
• Weight: 2
• Dimension: 395
• Nonzero newspaces: 15
• Newform subspaces: 37
• Sturm bound: 6048
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 37 \)
Sturm bound:			\(6048\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(234))\).

	Total	New	Old
Modular forms	1704	395	1309
Cusp forms	1321	395	926
Eisenstein series	383	0	383

Trace form

395 * q + 2 * q^2 + 6 * q^3 + 2 * q^4 - 6 * q^6 + 8 * q^7 - q^8 - 6 * q^9 + 15 * q^10 + 6 * q^11 + 26 * q^13 + 16 * q^14 + 6 * q^16 + 27 * q^17 + 12 * q^18 + 32 * q^19 + 3 * q^20 - 12 * q^21 - 6 * q^22 + 6 * q^24 + 5 * q^25 - 4 * q^26 - 20 * q^28 - 45 * q^29 - 48 * q^30 - 80 * q^31 + 2 * q^32 - 54 * q^33 - 78 * q^34 - 168 * q^35 - 54 * q^36 - 65 * q^37 - 110 * q^38 - 96 * q^39 - 123 * q^41 - 72 * q^42 - 70 * q^43 - 60 * q^44 - 120 * q^45 - 48 * q^46 - 108 * q^47 - 6 * q^48 - 86 * q^49 - 79 * q^50 - 66 * q^51 - 7 * q^52 - 12 * q^53 - 18 * q^54 + 60 * q^55 + 16 * q^56 - 6 * q^57 + 39 * q^58 + 54 * q^59 + 55 * q^61 + 52 * q^62 - 24 * q^63 - q^64 - 57 * q^65 - 10 * q^67 - 3 * q^68 - 72 * q^69 + 36 * q^70 - 72 * q^71 - 6 * q^72 - 148 * q^73 + 31 * q^74 - 90 * q^75 + 26 * q^76 - 84 * q^77 + 6 * q^78 - 8 * q^79 + 3 * q^80 - 78 * q^81 + 15 * q^82 - 120 * q^83 + 12 * q^84 - 69 * q^85 + 22 * q^86 - 132 * q^87 - 6 * q^88 - 72 * q^89 - 28 * q^91 + 12 * q^92 - 72 * q^93 + 48 * q^94 - 24 * q^95 + 70 * q^97 + 108 * q^98 + 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)

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
234.2.a	\(\chi_{234}(1, \cdot)\)	234.2.a.a	1	1
		234.2.a.b	1
		234.2.a.c	1
		234.2.a.d	1
		234.2.a.e	1
234.2.b	\(\chi_{234}(181, \cdot)\)	234.2.b.a	2	1
		234.2.b.b	2
234.2.e	\(\chi_{234}(79, \cdot)\)	234.2.e.a	2	2
		234.2.e.b	4
		234.2.e.c	4
		234.2.e.d	6
		234.2.e.e	8
234.2.f	\(\chi_{234}(133, \cdot)\)	234.2.f.a	2	2
		234.2.f.b	2
		234.2.f.c	12
		234.2.f.d	12
234.2.g	\(\chi_{234}(61, \cdot)\)	234.2.g.a	2	2
		234.2.g.b	2
		234.2.g.c	12
		234.2.g.d	12
234.2.h	\(\chi_{234}(55, \cdot)\)	234.2.h.a	2	2
		234.2.h.b	2
		234.2.h.c	2
		234.2.h.d	4
		234.2.h.e	4
234.2.j	\(\chi_{234}(125, \cdot)\)	234.2.j.a	4	2
234.2.l	\(\chi_{234}(127, \cdot)\)	234.2.l.a	4	2
		234.2.l.b	4
		234.2.l.c	4
234.2.p	\(\chi_{234}(43, \cdot)\)	234.2.p.a	28	2
234.2.s	\(\chi_{234}(121, \cdot)\)	234.2.s.a	28	2
234.2.t	\(\chi_{234}(25, \cdot)\)	234.2.t.a	28	2
234.2.x	\(\chi_{234}(71, \cdot)\)	234.2.x.a	8	4
		234.2.x.b	16
234.2.y	\(\chi_{234}(11, \cdot)\)	234.2.y.a	56	4
234.2.z	\(\chi_{234}(41, \cdot)\)	234.2.z.a	56	4
234.2.bd	\(\chi_{234}(5, \cdot)\)	234.2.bd.a	56	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(234))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(234)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)