Space of modular forms of level 462 and weight 2

• Label: 462.2
• Level: 462
• Weight: 2
• Dimension: 1353
• Nonzero newspaces: 16
• Newform subspaces: 61
• Sturm bound: 23040
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 61 \)
Sturm bound:			\(23040\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(462))\).

	Total	New	Old
Modular forms	6240	1353	4887
Cusp forms	5281	1353	3928
Eisenstein series	959	0	959

Trace form

1353 * q - 3 * q^2 + q^3 + 5 * q^4 + 6 * q^5 + 19 * q^6 + 37 * q^7 - 3 * q^8 + 53 * q^9 + 46 * q^10 + 41 * q^11 + 21 * q^12 + 30 * q^13 + 5 * q^14 + 42 * q^15 - 3 * q^16 + 50 * q^17 - 17 * q^18 + 32 * q^19 - 18 * q^20 - 15 * q^21 - 23 * q^22 - 8 * q^23 - 25 * q^24 + 35 * q^25 - 18 * q^26 - 59 * q^27 + 9 * q^28 - 2 * q^29 - 54 * q^30 + 24 * q^31 - 3 * q^32 - 89 * q^33 - 6 * q^34 + 26 * q^35 + 3 * q^36 - 2 * q^37 + 12 * q^38 - 6 * q^39 + 6 * q^40 + 10 * q^41 + 35 * q^42 + 148 * q^43 + 41 * q^44 + 6 * q^45 + 104 * q^46 + 88 * q^47 + q^48 + 117 * q^49 + 83 * q^50 + 32 * q^51 + 22 * q^52 + 30 * q^53 - 19 * q^54 + 98 * q^55 + 9 * q^56 + 6 * q^57 + 46 * q^58 + 36 * q^59 - 2 * q^60 - 26 * q^61 - 48 * q^62 - 217 * q^63 + 5 * q^64 - 204 * q^65 - 143 * q^66 - 196 * q^67 - 70 * q^68 - 264 * q^69 - 370 * q^70 - 392 * q^71 - 59 * q^72 - 318 * q^73 - 202 * q^74 - 407 * q^75 - 108 * q^76 - 267 * q^77 - 154 * q^78 - 240 * q^79 - 74 * q^80 - 291 * q^81 - 202 * q^82 - 252 * q^83 - 83 * q^84 - 300 * q^85 - 252 * q^86 - 270 * q^87 - 91 * q^88 - 198 * q^89 - 254 * q^90 - 386 * q^91 - 24 * q^92 - 160 * q^93 - 200 * q^94 - 144 * q^95 - 15 * q^96 - 34 * q^97 - 51 * q^98 - 83 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)

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
462.2.a	\(\chi_{462}(1, \cdot)\)	462.2.a.a	1	1
		462.2.a.b	1
		462.2.a.c	1
		462.2.a.d	1
		462.2.a.e	1
		462.2.a.f	1
		462.2.a.g	1
		462.2.a.h	2
462.2.c	\(\chi_{462}(197, \cdot)\)	462.2.c.a	12	1
		462.2.c.b	12
462.2.e	\(\chi_{462}(307, \cdot)\)	462.2.e.a	8	1
		462.2.e.b	8
462.2.g	\(\chi_{462}(419, \cdot)\)	462.2.g.a	4	1
		462.2.g.b	4
		462.2.g.c	4
		462.2.g.d	4
		462.2.g.e	8
462.2.i	\(\chi_{462}(67, \cdot)\)	462.2.i.a	2	2
		462.2.i.b	2
		462.2.i.c	2
		462.2.i.d	2
		462.2.i.e	4
		462.2.i.f	6
		462.2.i.g	6
462.2.j	\(\chi_{462}(169, \cdot)\)	462.2.j.a	4	4
		462.2.j.b	4
		462.2.j.c	4
		462.2.j.d	4
		462.2.j.e	8
		462.2.j.f	8
		462.2.j.g	8
		462.2.j.h	8
462.2.k	\(\chi_{462}(89, \cdot)\)	462.2.k.a	4	2
		462.2.k.b	4
		462.2.k.c	4
		462.2.k.d	8
		462.2.k.e	8
		462.2.k.f	8
		462.2.k.g	20
462.2.n	\(\chi_{462}(65, \cdot)\)	462.2.n.a	4	2
		462.2.n.b	4
		462.2.n.c	4
		462.2.n.d	4
		462.2.n.e	24
		462.2.n.f	24
462.2.p	\(\chi_{462}(241, \cdot)\)	462.2.p.a	16	2
		462.2.p.b	16
462.2.s	\(\chi_{462}(125, \cdot)\)	462.2.s.a	128	4
462.2.u	\(\chi_{462}(13, \cdot)\)	462.2.u.a	32	4
		462.2.u.b	32
462.2.w	\(\chi_{462}(29, \cdot)\)	462.2.w.a	48	4
		462.2.w.b	48
462.2.y	\(\chi_{462}(25, \cdot)\)	462.2.y.a	24	8
		462.2.y.b	24
		462.2.y.c	40
		462.2.y.d	40
462.2.ba	\(\chi_{462}(19, \cdot)\)	462.2.ba.a	64	8
		462.2.ba.b	64
462.2.bc	\(\chi_{462}(95, \cdot)\)	462.2.bc.a	128	8
		462.2.bc.b	128
462.2.bf	\(\chi_{462}(5, \cdot)\)	462.2.bf.a	256	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(462))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(462)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 1}\)