Space of modular forms of level 418 and weight 2

• Label: 418.2
• Level: 418
• Weight: 2
• Dimension: 1763
• Nonzero newspaces: 12
• Newform subspaces: 50
• Sturm bound: 21600
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 50 \)
Sturm bound:			\(21600\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(418))\).

	Total	New	Old
Modular forms	5760	1763	3997
Cusp forms	5041	1763	3278
Eisenstein series	719	0	719

Trace form

1763 * q + 3 * q^2 + 12 * q^3 + 3 * q^4 + 18 * q^5 + 2 * q^6 + 4 * q^7 + 3 * q^8 - q^9 - 2 * q^10 + 3 * q^11 - 20 * q^12 - 26 * q^13 - 32 * q^14 - 60 * q^15 + 3 * q^16 - 22 * q^17 - 25 * q^18 - 60 * q^19 - 18 * q^20 - 28 * q^21 - 4 * q^22 - 4 * q^23 + 2 * q^24 - 59 * q^25 - 34 * q^26 - 36 * q^27 - 8 * q^28 - 26 * q^29 + 12 * q^30 - 7 * q^32 - 72 * q^33 + 14 * q^34 - 48 * q^35 + 29 * q^36 + 38 * q^37 + 9 * q^38 - 40 * q^39 - 2 * q^40 + 10 * q^41 + 36 * q^42 - 52 * q^43 - 16 * q^44 - 82 * q^45 - 40 * q^46 - 80 * q^47 - 6 * q^48 - 69 * q^49 - 91 * q^50 - 112 * q^51 - 10 * q^52 - 82 * q^53 - 68 * q^54 - 74 * q^55 - 48 * q^56 - 109 * q^57 - 62 * q^58 - 130 * q^59 - 40 * q^60 - 110 * q^61 - 72 * q^62 - 120 * q^63 - 9 * q^64 - 164 * q^65 - 100 * q^66 - 132 * q^67 - 4 * q^68 - 40 * q^69 - 8 * q^70 - 88 * q^71 - 19 * q^72 + 36 * q^73 + 74 * q^74 + 58 * q^75 + 29 * q^76 - 12 * q^77 + 16 * q^78 - 16 * q^79 - 2 * q^80 - 105 * q^81 - 16 * q^82 - 22 * q^83 - 92 * q^84 - 40 * q^85 - 70 * q^86 - 200 * q^87 + 3 * q^88 - 34 * q^89 - 126 * q^90 - 56 * q^91 - 60 * q^92 - 176 * q^93 - 120 * q^94 - 56 * q^95 + 12 * q^96 - 76 * q^97 - 63 * q^98 - 168 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(418))\)

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
418.2.a	\(\chi_{418}(1, \cdot)\)	418.2.a.a	1	1
		418.2.a.b	1
		418.2.a.c	1
		418.2.a.d	2
		418.2.a.e	2
		418.2.a.f	2
		418.2.a.g	3
		418.2.a.h	3
418.2.b	\(\chi_{418}(417, \cdot)\)	418.2.b.a	2	1
		418.2.b.b	2
		418.2.b.c	8
		418.2.b.d	8
418.2.e	\(\chi_{418}(45, \cdot)\)	418.2.e.a	2	2
		418.2.e.b	2
		418.2.e.c	2
		418.2.e.d	2
		418.2.e.e	2
		418.2.e.f	2
		418.2.e.g	4
		418.2.e.h	6
		418.2.e.i	6
418.2.f	\(\chi_{418}(115, \cdot)\)	418.2.f.a	4	4
		418.2.f.b	4
		418.2.f.c	4
		418.2.f.d	4
		418.2.f.e	4
		418.2.f.f	16
		418.2.f.g	16
		418.2.f.h	20
418.2.h	\(\chi_{418}(65, \cdot)\)	418.2.h.a	20	2
		418.2.h.b	20
418.2.j	\(\chi_{418}(23, \cdot)\)	418.2.j.a	24	6
		418.2.j.b	24
		418.2.j.c	30
		418.2.j.d	30
418.2.m	\(\chi_{418}(151, \cdot)\)	418.2.m.a	40	4
		418.2.m.b	40
418.2.n	\(\chi_{418}(49, \cdot)\)	418.2.n.a	8	8
		418.2.n.b	8
		418.2.n.c	8
		418.2.n.d	64
		418.2.n.e	72
418.2.q	\(\chi_{418}(21, \cdot)\)	418.2.q.a	60	6
		418.2.q.b	60
418.2.s	\(\chi_{418}(107, \cdot)\)	418.2.s.a	80	8
		418.2.s.b	80
418.2.u	\(\chi_{418}(5, \cdot)\)	418.2.u.a	216	24
		418.2.u.b	264
418.2.v	\(\chi_{418}(13, \cdot)\)	418.2.v.a	240	24
		418.2.v.b	240

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(418))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(418)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 2}\)