Space of modular forms of level 351 and weight 2

• Label: 351.2
• Level: 351
• Weight: 2
• Dimension: 3366
• Nonzero newspaces: 24
• Newform subspaces: 61
• Sturm bound: 18144
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Newform subspaces:			\( 61 \)
Sturm bound:			\(18144\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(351))\).

	Total	New	Old
Modular forms	4896	3718	1178
Cusp forms	4177	3366	811
Eisenstein series	719	352	367

Trace form

3366 * q - 36 * q^2 - 60 * q^3 - 68 * q^4 - 42 * q^5 - 72 * q^6 - 70 * q^7 - 60 * q^8 - 72 * q^9 - 78 * q^10 - 54 * q^11 - 96 * q^12 - 83 * q^13 - 126 * q^14 - 90 * q^15 - 92 * q^16 - 66 * q^17 - 90 * q^18 - 64 * q^19 - 42 * q^20 - 48 * q^21 - 90 * q^22 - 24 * q^23 - 36 * q^24 - 80 * q^25 - 18 * q^26 - 126 * q^27 - 188 * q^28 - 60 * q^29 - 54 * q^30 - 110 * q^31 - 120 * q^32 - 72 * q^33 - 150 * q^34 - 132 * q^35 - 108 * q^36 - 128 * q^37 - 216 * q^38 - 105 * q^39 - 306 * q^40 - 126 * q^41 - 108 * q^42 - 134 * q^43 - 150 * q^44 - 54 * q^45 - 126 * q^46 - 54 * q^47 - 42 * q^48 - 124 * q^49 - 54 * q^50 - 36 * q^51 - 99 * q^52 - 60 * q^53 + 36 * q^54 - 168 * q^55 - 30 * q^56 - 66 * q^57 - 126 * q^58 - 24 * q^59 - 72 * q^60 - 106 * q^61 - 60 * q^62 - 90 * q^63 - 164 * q^64 - 123 * q^65 - 126 * q^66 - 112 * q^67 - 222 * q^68 - 90 * q^69 - 198 * q^70 - 198 * q^71 - 108 * q^72 - 178 * q^73 - 282 * q^74 - 150 * q^75 - 88 * q^76 - 186 * q^77 - 90 * q^78 - 166 * q^79 - 384 * q^80 - 144 * q^81 - 288 * q^82 - 246 * q^83 - 84 * q^84 - 126 * q^85 - 306 * q^86 - 90 * q^87 - 168 * q^88 - 138 * q^89 - 108 * q^90 - 133 * q^91 - 138 * q^92 + 6 * q^93 - 126 * q^94 - 30 * q^95 + 216 * q^96 - 8 * q^97 + 198 * q^98 + 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)

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
351.2.a	\(\chi_{351}(1, \cdot)\)	351.2.a.a	2	1
		351.2.a.b	2
		351.2.a.c	2
		351.2.a.d	2
		351.2.a.e	4
		351.2.a.f	4
351.2.b	\(\chi_{351}(298, \cdot)\)	351.2.b.a	2	1
		351.2.b.b	4
		351.2.b.c	4
		351.2.b.d	4
		351.2.b.e	4
351.2.e	\(\chi_{351}(118, \cdot)\)	351.2.e.a	2	2
		351.2.e.b	10
		351.2.e.c	12
351.2.f	\(\chi_{351}(100, \cdot)\)	351.2.f.a	24	2
351.2.g	\(\chi_{351}(55, \cdot)\)	351.2.g.a	2	2
		351.2.g.b	2
		351.2.g.c	2
		351.2.g.d	10
		351.2.g.e	10
		351.2.g.f	12
351.2.h	\(\chi_{351}(289, \cdot)\)	351.2.h.a	24	2
351.2.i	\(\chi_{351}(161, \cdot)\)	351.2.i.a	4	2
		351.2.i.b	16
		351.2.i.c	16
351.2.l	\(\chi_{351}(127, \cdot)\)	351.2.l.a	2	2
		351.2.l.b	22
351.2.q	\(\chi_{351}(82, \cdot)\)	351.2.q.a	2	2
		351.2.q.b	2
		351.2.q.c	2
		351.2.q.d	2
		351.2.q.e	2
		351.2.q.f	4
		351.2.q.g	8
		351.2.q.h	8
		351.2.q.i	8
351.2.r	\(\chi_{351}(10, \cdot)\)	351.2.r.a	2	2
		351.2.r.b	22
351.2.t	\(\chi_{351}(64, \cdot)\)	351.2.t.a	2	2
		351.2.t.b	2
		351.2.t.c	20
351.2.w	\(\chi_{351}(40, \cdot)\)	351.2.w.a	6	6
		351.2.w.b	102
		351.2.w.c	108
351.2.x	\(\chi_{351}(16, \cdot)\)	351.2.x.a	240	6
351.2.y	\(\chi_{351}(61, \cdot)\)	351.2.y.a	240	6
351.2.ba	\(\chi_{351}(71, \cdot)\)	351.2.ba.a	48	4
351.2.bc	\(\chi_{351}(8, \cdot)\)	351.2.bc.a	4	4
		351.2.bc.b	44
351.2.bd	\(\chi_{351}(80, \cdot)\)	351.2.bd.a	4	4
		351.2.bd.b	16
		351.2.bd.c	16
		351.2.bd.d	20
		351.2.bd.e	20
351.2.bf	\(\chi_{351}(206, \cdot)\)	351.2.bf.a	48	4
351.2.bl	\(\chi_{351}(25, \cdot)\)	351.2.bl.a	240	6
351.2.bn	\(\chi_{351}(4, \cdot)\)	351.2.bn.a	240	6
351.2.bo	\(\chi_{351}(43, \cdot)\)	351.2.bo.a	240	6
351.2.bq	\(\chi_{351}(20, \cdot)\)	351.2.bq.a	480	12
351.2.bt	\(\chi_{351}(5, \cdot)\)	351.2.bt.a	480	12
351.2.bv	\(\chi_{351}(2, \cdot)\)	351.2.bv.a	480	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(351))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(351)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)