Space of modular forms of level 460 and weight 2

• Label: 460.2
• Level: 460
• Weight: 2
• Dimension: 3250
• Nonzero newspaces: 12
• Newform subspaces: 22
• Sturm bound: 25344
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 22 \)
Sturm bound:			\(25344\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(460))\).

	Total	New	Old
Modular forms	6776	3498	3278
Cusp forms	5897	3250	2647
Eisenstein series	879	248	631

Trace form

3250 * q - 18 * q^2 + 4 * q^3 - 22 * q^4 - 56 * q^5 - 66 * q^6 - 4 * q^7 - 30 * q^8 - 46 * q^9 - 45 * q^10 - 22 * q^12 - 44 * q^13 - 22 * q^14 + 7 * q^15 - 50 * q^16 - 22 * q^17 - 10 * q^18 + 30 * q^19 - 25 * q^20 - 58 * q^21 - 44 * q^22 + 38 * q^23 - 44 * q^24 - 58 * q^25 - 74 * q^26 + 58 * q^27 - 22 * q^28 - 34 * q^29 - 33 * q^30 + 30 * q^31 - 38 * q^32 - 22 * q^33 - 66 * q^34 - 18 * q^35 - 200 * q^36 - 108 * q^37 - 132 * q^38 - 80 * q^39 - 113 * q^40 - 156 * q^41 - 242 * q^42 - 68 * q^43 - 176 * q^44 - 164 * q^45 - 242 * q^46 - 76 * q^47 - 198 * q^48 - 170 * q^49 - 27 * q^50 - 112 * q^51 - 234 * q^52 - 112 * q^53 - 198 * q^54 - 22 * q^55 - 176 * q^56 - 82 * q^57 - 148 * q^58 + 20 * q^59 - 55 * q^60 - 96 * q^61 - 22 * q^62 + 106 * q^63 - 22 * q^64 + 11 * q^65 + 40 * q^67 - 20 * q^68 + 78 * q^69 - 66 * q^70 + 134 * q^71 - 64 * q^72 + 40 * q^73 + 59 * q^75 + 44 * q^76 - 110 * q^77 + 198 * q^78 + 28 * q^79 + 34 * q^80 - 250 * q^81 + 78 * q^82 + 10 * q^83 + 286 * q^84 - 174 * q^85 + 154 * q^86 - 108 * q^87 + 154 * q^88 - 164 * q^89 + 142 * q^90 - 96 * q^91 + 176 * q^92 - 632 * q^93 + 132 * q^94 - 85 * q^95 + 352 * q^96 - 298 * q^97 + 126 * q^98 - 242 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)

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
460.2.a	\(\chi_{460}(1, \cdot)\)	460.2.a.a	1	1
		460.2.a.b	1
		460.2.a.c	1
		460.2.a.d	1
		460.2.a.e	2
460.2.c	\(\chi_{460}(369, \cdot)\)	460.2.c.a	12	1
460.2.e	\(\chi_{460}(91, \cdot)\)	460.2.e.a	16	1
		460.2.e.b	32
460.2.g	\(\chi_{460}(459, \cdot)\)	460.2.g.a	4	1
		460.2.g.b	8
		460.2.g.c	56
460.2.i	\(\chi_{460}(137, \cdot)\)	460.2.i.a	8	2
		460.2.i.b	16
460.2.j	\(\chi_{460}(47, \cdot)\)	460.2.j.a	132	2
460.2.m	\(\chi_{460}(41, \cdot)\)	460.2.m.a	30	10
		460.2.m.b	50
460.2.o	\(\chi_{460}(19, \cdot)\)	460.2.o.a	40	10
		460.2.o.b	640
460.2.q	\(\chi_{460}(11, \cdot)\)	460.2.q.a	480	10
460.2.s	\(\chi_{460}(9, \cdot)\)	460.2.s.a	120	10
460.2.w	\(\chi_{460}(3, \cdot)\)	460.2.w.a	1360	20
460.2.x	\(\chi_{460}(17, \cdot)\)	460.2.x.a	240	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(460))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(460)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 1}\)