Space of modular forms of level 342 and weight 2

• Label: 342.2
• Level: 342
• Weight: 2
• Dimension: 851
• Nonzero newspaces: 16
• Newform subspaces: 68
• Sturm bound: 12960
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 68 \)
Sturm bound:			\(12960\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(342))\).

	Total	New	Old
Modular forms	3528	851	2677
Cusp forms	2953	851	2102
Eisenstein series	575	0	575

Trace form

851 * q + 2 * q^2 + 6 * q^3 + 2 * q^4 - 6 * q^6 + 4 * q^7 - 4 * q^8 - 6 * q^9 - 6 * q^11 + 28 * q^13 + 22 * q^14 + 2 * q^16 + 30 * q^17 + 12 * q^18 + 44 * q^19 + 18 * q^20 - 12 * q^21 + 21 * q^22 + 6 * q^23 + 6 * q^24 + 26 * q^25 + 10 * q^26 - 2 * q^28 + 30 * q^29 + 10 * q^31 + 2 * q^32 + 18 * q^33 - 6 * q^34 + 36 * q^35 - 6 * q^36 + 34 * q^37 - q^38 + 36 * q^41 + 16 * q^43 - 15 * q^44 - 108 * q^45 - 84 * q^46 - 156 * q^47 - 24 * q^48 - 114 * q^49 - 226 * q^50 - 198 * q^51 - 14 * q^52 - 264 * q^53 - 126 * q^54 - 216 * q^55 - 104 * q^56 - 183 * q^57 - 96 * q^58 - 264 * q^59 - 72 * q^60 - 194 * q^61 - 146 * q^62 - 120 * q^63 - 22 * q^64 - 252 * q^65 - 144 * q^66 - 80 * q^67 - 33 * q^68 - 108 * q^69 - 108 * q^70 - 96 * q^71 - 24 * q^72 - 35 * q^73 - 8 * q^74 + 30 * q^75 - q^76 + 24 * q^77 + 12 * q^78 + 70 * q^79 + 18 * q^81 + 96 * q^83 + 12 * q^84 + 72 * q^85 + 34 * q^86 - 36 * q^87 - 6 * q^88 + 48 * q^89 + 80 * q^91 + 24 * q^92 + 60 * q^94 - 54 * q^95 - 44 * q^97 + 84 * q^98 - 162 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)

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
342.2.a	\(\chi_{342}(1, \cdot)\)	342.2.a.a	1	1
		342.2.a.b	1
		342.2.a.c	1
		342.2.a.d	1
		342.2.a.e	1
		342.2.a.f	1
		342.2.a.g	1
342.2.b	\(\chi_{342}(341, \cdot)\)	342.2.b.a	2	1
		342.2.b.b	2
342.2.e	\(\chi_{342}(115, \cdot)\)	342.2.e.a	6	2
		342.2.e.b	6
		342.2.e.c	12
		342.2.e.d	12
342.2.f	\(\chi_{342}(7, \cdot)\)	342.2.f.a	2	2
		342.2.f.b	2
		342.2.f.c	2
		342.2.f.d	2
		342.2.f.e	4
		342.2.f.f	10
		342.2.f.g	18
342.2.g	\(\chi_{342}(163, \cdot)\)	342.2.g.a	2	2
		342.2.g.b	2
		342.2.g.c	2
		342.2.g.d	2
		342.2.g.e	2
		342.2.g.f	4
342.2.h	\(\chi_{342}(121, \cdot)\)	342.2.h.a	2	2
		342.2.h.b	2
		342.2.h.c	2
		342.2.h.d	2
		342.2.h.e	4
		342.2.h.f	10
		342.2.h.g	18
342.2.j	\(\chi_{342}(65, \cdot)\)	342.2.j.a	2	2
		342.2.j.b	2
		342.2.j.c	2
		342.2.j.d	8
		342.2.j.e	8
		342.2.j.f	18
342.2.n	\(\chi_{342}(293, \cdot)\)	342.2.n.a	2	2
		342.2.n.b	2
		342.2.n.c	2
		342.2.n.d	8
		342.2.n.e	8
		342.2.n.f	18
342.2.p	\(\chi_{342}(113, \cdot)\)	342.2.p.a	20	2
		342.2.p.b	20
342.2.s	\(\chi_{342}(107, \cdot)\)	342.2.s.a	4	2
		342.2.s.b	4
342.2.u	\(\chi_{342}(55, \cdot)\)	342.2.u.a	6	6
		342.2.u.b	6
		342.2.u.c	6
		342.2.u.d	6
		342.2.u.e	6
		342.2.u.f	12
		342.2.u.g	12
342.2.v	\(\chi_{342}(25, \cdot)\)	342.2.v.a	54	6
		342.2.v.b	66
342.2.w	\(\chi_{342}(43, \cdot)\)	342.2.w.a	54	6
		342.2.w.b	66
342.2.x	\(\chi_{342}(29, \cdot)\)	342.2.x.a	12	6
		342.2.x.b	48
		342.2.x.c	60
342.2.bb	\(\chi_{342}(53, \cdot)\)	342.2.bb.a	24	6
		342.2.bb.b	24
342.2.bf	\(\chi_{342}(155, \cdot)\)	342.2.bf.a	12	6
		342.2.bf.b	48
		342.2.bf.c	60

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(342)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)