Space of modular forms of level 459 and weight 2

• Label: 459.2
• Level: 459
• Weight: 2
• Dimension: 5862
• Nonzero newspaces: 15
• Newform subspaces: 38
• Sturm bound: 31104
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 38 \)
Sturm bound:			\(31104\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(459))\).

	Total	New	Old
Modular forms	8256	6342	1914
Cusp forms	7297	5862	1435
Eisenstein series	959	480	479

Trace form

5862 * q - 52 * q^2 - 84 * q^3 - 96 * q^4 - 58 * q^5 - 96 * q^6 - 98 * q^7 - 76 * q^8 - 96 * q^9 - 106 * q^10 - 70 * q^11 - 120 * q^12 - 110 * q^13 - 94 * q^14 - 114 * q^15 - 120 * q^16 - 73 * q^17 - 210 * q^18 - 92 * q^19 - 58 * q^20 - 72 * q^21 - 118 * q^22 - 40 * q^23 - 60 * q^24 - 108 * q^25 - 4 * q^26 - 78 * q^27 - 236 * q^28 - 52 * q^29 - 78 * q^30 - 110 * q^31 - 96 * q^32 - 96 * q^33 - 121 * q^34 - 152 * q^35 - 132 * q^36 - 128 * q^37 - 164 * q^38 - 162 * q^39 - 218 * q^40 - 142 * q^41 - 132 * q^42 - 166 * q^43 - 198 * q^44 - 78 * q^45 - 170 * q^46 - 114 * q^47 - 66 * q^48 - 188 * q^49 - 126 * q^50 - 78 * q^51 - 350 * q^52 - 92 * q^53 + 12 * q^54 - 296 * q^55 - 158 * q^56 - 90 * q^57 - 218 * q^58 - 104 * q^59 - 96 * q^60 - 166 * q^61 - 136 * q^62 - 114 * q^63 - 184 * q^64 - 102 * q^65 - 78 * q^66 - 92 * q^67 - 73 * q^68 - 210 * q^69 - 82 * q^70 - 118 * q^71 - 132 * q^72 - 110 * q^73 - 130 * q^74 - 174 * q^75 - 44 * q^76 - 94 * q^77 - 132 * q^78 - 62 * q^79 - 228 * q^80 - 168 * q^81 - 232 * q^82 - 158 * q^83 - 108 * q^84 - 149 * q^85 - 390 * q^86 - 114 * q^87 - 180 * q^88 - 178 * q^89 - 132 * q^90 - 242 * q^91 - 210 * q^92 - 18 * q^93 - 274 * q^94 - 158 * q^95 - 96 * q^96 - 144 * q^97 - 246 * q^98 - 42 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(459))\)

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
459.2.a	\(\chi_{459}(1, \cdot)\)	459.2.a.a	1	1
		459.2.a.b	1
		459.2.a.c	1
		459.2.a.d	1
		459.2.a.e	1
		459.2.a.f	1
		459.2.a.g	1
		459.2.a.h	1
		459.2.a.i	2
		459.2.a.j	2
		459.2.a.k	2
		459.2.a.l	2
		459.2.a.m	3
		459.2.a.n	3
459.2.d	\(\chi_{459}(271, \cdot)\)	459.2.d.a	4	1
		459.2.d.b	8
		459.2.d.c	12
459.2.e	\(\chi_{459}(154, \cdot)\)	459.2.e.a	4	2
		459.2.e.b	8
		459.2.e.c	20
459.2.f	\(\chi_{459}(55, \cdot)\)	459.2.f.a	4	2
		459.2.f.b	20
		459.2.f.c	24
459.2.h	\(\chi_{459}(118, \cdot)\)	459.2.h.a	8	2
		459.2.h.b	24
459.2.l	\(\chi_{459}(298, \cdot)\)	459.2.l.a	48	4
		459.2.l.b	48
459.2.m	\(\chi_{459}(52, \cdot)\)	459.2.m.a	132	6
		459.2.m.b	156
459.2.o	\(\chi_{459}(64, \cdot)\)	459.2.o.a	64	4
459.2.p	\(\chi_{459}(80, \cdot)\)	459.2.p.a	96	8
		459.2.p.b	96
459.2.r	\(\chi_{459}(16, \cdot)\)	459.2.r.a	312	6
459.2.v	\(\chi_{459}(19, \cdot)\)	459.2.v.a	128	8
459.2.x	\(\chi_{459}(4, \cdot)\)	459.2.x.a	624	12
459.2.y	\(\chi_{459}(44, \cdot)\)	459.2.y.a	256	16
459.2.ba	\(\chi_{459}(25, \cdot)\)	459.2.ba.a	1248	24
459.2.bd	\(\chi_{459}(5, \cdot)\)	459.2.bd.a	2496	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(459))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(459)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(459))\)\(^{\oplus 1}\)