Space of modular forms of level 522 and weight 2

• Label: 522.2
• Level: 522
• Weight: 2
• Dimension: 1991
• Nonzero newspaces: 12
• Newform subspaces: 50
• Sturm bound: 30240
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 522 = 2 \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 50 \)
Sturm bound:			\(30240\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(522))\).

	Total	New	Old
Modular forms	8008	1991	6017
Cusp forms	7113	1991	5122
Eisenstein series	895	0	895

Trace form

1991 * q + 2 * q^2 + 6 * q^3 + 2 * q^4 - 6 * q^6 + 4 * q^7 - 4 * q^8 - 6 * q^9 - 6 * q^11 + 4 * q^13 + 4 * q^14 + 2 * q^16 + 12 * q^17 + 12 * q^18 + 4 * q^19 + 7 * q^20 - 12 * q^21 + 22 * q^22 + 16 * q^23 + 6 * q^24 + 46 * q^25 + 27 * q^26 - 8 * q^28 + 62 * q^29 + 48 * q^31 + 2 * q^32 + 18 * q^33 + 29 * q^34 + 56 * q^35 - 6 * q^36 + 44 * q^37 + 26 * q^38 + 7 * q^40 + 18 * q^41 - 2 * q^43 + 12 * q^44 + 24 * q^46 + 16 * q^47 - 6 * q^48 + 50 * q^49 - 10 * q^50 - 18 * q^51 + 4 * q^52 + 15 * q^53 - 18 * q^54 + 112 * q^55 + 4 * q^56 - 6 * q^57 + 6 * q^58 + 34 * q^59 + 72 * q^61 + 16 * q^62 + 24 * q^63 - 4 * q^64 + 63 * q^65 + 66 * q^67 - 6 * q^68 - 84 * q^70 - 176 * q^71 - 6 * q^72 - 177 * q^73 - 260 * q^74 - 250 * q^75 - 170 * q^76 - 432 * q^77 - 212 * q^78 - 176 * q^79 - 430 * q^81 - 204 * q^82 - 312 * q^83 - 156 * q^84 - 504 * q^85 - 422 * q^86 - 298 * q^87 - 6 * q^88 - 444 * q^89 - 280 * q^90 - 520 * q^91 - 264 * q^92 - 224 * q^93 - 180 * q^94 - 672 * q^95 - 151 * q^97 - 324 * q^98 - 316 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(522))\)

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
522.2.a	\(\chi_{522}(1, \cdot)\)	522.2.a.a	1	1
		522.2.a.b	1
		522.2.a.c	1
		522.2.a.d	1
		522.2.a.e	1
		522.2.a.f	1
		522.2.a.g	1
		522.2.a.h	1
		522.2.a.i	1
		522.2.a.j	1
		522.2.a.k	1
		522.2.a.l	1
		522.2.a.m	1
522.2.d	\(\chi_{522}(289, \cdot)\)	522.2.d.a	2	1
		522.2.d.b	2
		522.2.d.c	4
		522.2.d.d	4
522.2.e	\(\chi_{522}(175, \cdot)\)	522.2.e.a	2	2
		522.2.e.b	2
		522.2.e.c	2
		522.2.e.d	2
		522.2.e.e	4
		522.2.e.f	6
		522.2.e.g	8
		522.2.e.h	12
		522.2.e.i	18
522.2.g	\(\chi_{522}(17, \cdot)\)	522.2.g.a	8	2
		522.2.g.b	12
522.2.h	\(\chi_{522}(115, \cdot)\)	522.2.h.a	4	2
		522.2.h.b	56
522.2.k	\(\chi_{522}(181, \cdot)\)	522.2.k.a	6	6
		522.2.k.b	6
		522.2.k.c	6
		522.2.k.d	6
		522.2.k.e	6
		522.2.k.f	12
		522.2.k.g	12
		522.2.k.h	12
		522.2.k.i	12
522.2.l	\(\chi_{522}(41, \cdot)\)	522.2.l.a	120	4
522.2.n	\(\chi_{522}(91, \cdot)\)	522.2.n.a	12	6
		522.2.n.b	12
		522.2.n.c	24
		522.2.n.d	24
522.2.q	\(\chi_{522}(7, \cdot)\)	522.2.q.a	180	12
		522.2.q.b	180
522.2.r	\(\chi_{522}(89, \cdot)\)	522.2.r.a	48	12
		522.2.r.b	72
522.2.v	\(\chi_{522}(13, \cdot)\)	522.2.v.a	360	12
522.2.x	\(\chi_{522}(11, \cdot)\)	522.2.x.a	720	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(522))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(522)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 2}\)