Space of modular forms of level 828 and weight 2

• Label: 828.2
• Level: 828
• Weight: 2
• Dimension: 8554
• Nonzero newspaces: 16
• Newform subspaces: 43
• Sturm bound: 76032
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 43 \)
Sturm bound:			\(76032\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(828))\).

	Total	New	Old
Modular forms	19888	8934	10954
Cusp forms	18129	8554	9575
Eisenstein series	1759	380	1379

Trace form

8554 * q - 27 * q^2 - 23 * q^4 - 48 * q^5 - 38 * q^6 + 6 * q^7 - 33 * q^8 - 64 * q^9 - 91 * q^10 + 6 * q^11 - 56 * q^12 - 52 * q^13 - 57 * q^14 - 18 * q^15 - 47 * q^16 - 101 * q^17 - 80 * q^18 - 11 * q^19 - 69 * q^20 - 82 * q^21 - 28 * q^22 - 25 * q^23 - 94 * q^24 - 70 * q^25 - 33 * q^26 - 75 * q^28 - 83 * q^29 - 8 * q^30 + 7 * q^31 + 33 * q^32 - 118 * q^33 + 15 * q^34 + 34 * q^35 + 22 * q^36 - 134 * q^37 + 76 * q^38 + 6 * q^39 + 51 * q^40 - 86 * q^41 - 8 * q^42 + 26 * q^43 + 44 * q^44 - 118 * q^45 - 23 * q^46 + 26 * q^47 - 86 * q^48 - 38 * q^49 + 2 * q^50 + 13 * q^52 - 20 * q^53 - 122 * q^54 + 74 * q^55 - 14 * q^56 - 34 * q^57 - 42 * q^58 + 148 * q^59 - 56 * q^60 + 56 * q^61 - 33 * q^62 + 116 * q^63 - 119 * q^64 + 219 * q^65 + 4 * q^66 + 84 * q^67 - 36 * q^68 + 61 * q^69 - 54 * q^70 + 213 * q^71 - 2 * q^72 - 16 * q^73 + 16 * q^74 + 178 * q^75 - 82 * q^76 + 241 * q^77 - 20 * q^78 + 184 * q^79 - 132 * q^80 + 24 * q^81 - 193 * q^82 + 103 * q^83 - 104 * q^84 + 134 * q^85 - 185 * q^86 + 18 * q^87 - 79 * q^88 - 24 * q^89 - 100 * q^90 + 56 * q^91 - 156 * q^92 - 266 * q^93 - 74 * q^94 + 9 * q^95 - 68 * q^96 - 79 * q^97 - 121 * q^98 - 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(828))\)

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
828.2.a	\(\chi_{828}(1, \cdot)\)	828.2.a.a	1	1
		828.2.a.b	1
		828.2.a.c	1
		828.2.a.d	1
		828.2.a.e	2
		828.2.a.f	2
828.2.c	\(\chi_{828}(323, \cdot)\)	828.2.c.a	2	1
		828.2.c.b	2
		828.2.c.c	8
		828.2.c.d	8
		828.2.c.e	12
		828.2.c.f	12
828.2.e	\(\chi_{828}(91, \cdot)\)	828.2.e.a	4	1
		828.2.e.b	6
		828.2.e.c	8
		828.2.e.d	8
		828.2.e.e	8
		828.2.e.f	24
828.2.g	\(\chi_{828}(413, \cdot)\)	828.2.g.a	8	1
828.2.i	\(\chi_{828}(277, \cdot)\)	828.2.i.a	6	2
		828.2.i.b	10
		828.2.i.c	12
		828.2.i.d	16
828.2.k	\(\chi_{828}(137, \cdot)\)	828.2.k.a	48	2
828.2.m	\(\chi_{828}(367, \cdot)\)	828.2.m.a	8	2
		828.2.m.b	12
		828.2.m.c	12
		828.2.m.d	248
828.2.o	\(\chi_{828}(47, \cdot)\)	828.2.o.a	132	2
		828.2.o.b	132
828.2.q	\(\chi_{828}(73, \cdot)\)	828.2.q.a	20	10
		828.2.q.b	20
		828.2.q.c	20
		828.2.q.d	40
828.2.s	\(\chi_{828}(17, \cdot)\)	828.2.s.a	80	10
828.2.u	\(\chi_{828}(19, \cdot)\)	828.2.u.a	100	10
		828.2.u.b	240
		828.2.u.c	240
828.2.w	\(\chi_{828}(35, \cdot)\)	828.2.w.a	480	10
828.2.y	\(\chi_{828}(13, \cdot)\)	828.2.y.a	480	20
828.2.ba	\(\chi_{828}(59, \cdot)\)	828.2.ba.a	2800	20
828.2.bc	\(\chi_{828}(7, \cdot)\)	828.2.bc.a	2800	20
828.2.be	\(\chi_{828}(5, \cdot)\)	828.2.be.a	480	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(828))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(828)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 2}\)