Space of modular forms of level 322 and weight 2

• Label: 322.2
• Level: 322
• Weight: 2
• Dimension: 1011
• Nonzero newspaces: 8
• Newform subspaces: 28
• Sturm bound: 12672
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 28 \)
Sturm bound:			\(12672\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(322))\).

	Total	New	Old
Modular forms	3432	1011	2421
Cusp forms	2905	1011	1894
Eisenstein series	527	0	527

Trace form

1011 * q + 3 * q^2 + 8 * q^3 - q^4 + 6 * q^5 - q^7 + 3 * q^8 + 11 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^12 + 22 * q^13 + 3 * q^14 - 20 * q^15 - q^16 - 38 * q^17 - 73 * q^18 - 28 * q^19 - 38 * q^20 - 58 * q^21 - 32 * q^22 - 65 * q^23 - 47 * q^25 - 38 * q^26 - 100 * q^27 - 23 * q^28 - 2 * q^29 - 64 * q^30 - 4 * q^31 + 3 * q^32 + 4 * q^33 + 30 * q^34 - 16 * q^35 + 11 * q^36 - 54 * q^37 + 24 * q^38 - 48 * q^39 + 6 * q^40 - 14 * q^41 - 60 * q^43 + 12 * q^44 - 54 * q^45 + 23 * q^46 - 16 * q^47 + 8 * q^48 - 67 * q^49 + 21 * q^50 + 8 * q^51 + 22 * q^52 - 2 * q^53 + 4 * q^54 - 104 * q^55 - 19 * q^56 - 132 * q^57 - 70 * q^58 - 148 * q^59 - 20 * q^60 - 130 * q^61 - 108 * q^62 - 99 * q^63 - q^64 - 224 * q^65 - 128 * q^66 - 12 * q^67 - 82 * q^68 - 128 * q^69 - 82 * q^70 - 148 * q^71 - 73 * q^72 - 18 * q^73 - 134 * q^74 - 248 * q^75 + 16 * q^76 - 98 * q^77 - 60 * q^78 - 156 * q^79 - 38 * q^80 - 121 * q^81 - 34 * q^82 - 80 * q^83 - 14 * q^84 - 24 * q^85 + 16 * q^86 - 36 * q^87 + 12 * q^88 + 58 * q^89 + 78 * q^90 - 22 * q^91 + 23 * q^92 + 112 * q^93 + 24 * q^94 - 12 * q^95 - 58 * q^97 - 41 * q^98 - 196 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)

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
322.2.a	\(\chi_{322}(1, \cdot)\)	322.2.a.a	1	1
		322.2.a.b	1
		322.2.a.c	1
		322.2.a.d	1
		322.2.a.e	2
		322.2.a.f	2
		322.2.a.g	3
322.2.c	\(\chi_{322}(321, \cdot)\)	322.2.c.a	4	1
		322.2.c.b	4
		322.2.c.c	4
		322.2.c.d	4
322.2.e	\(\chi_{322}(93, \cdot)\)	322.2.e.a	8	2
		322.2.e.b	8
		322.2.e.c	8
		322.2.e.d	8
322.2.g	\(\chi_{322}(45, \cdot)\)	322.2.g.a	16	2
		322.2.g.b	16
322.2.i	\(\chi_{322}(29, \cdot)\)	322.2.i.a	10	10
		322.2.i.b	10
		322.2.i.c	20
		322.2.i.d	40
		322.2.i.e	40
322.2.k	\(\chi_{322}(83, \cdot)\)	322.2.k.a	80	10
		322.2.k.b	80
322.2.m	\(\chi_{322}(9, \cdot)\)	322.2.m.a	160	20
		322.2.m.b	160
322.2.o	\(\chi_{322}(5, \cdot)\)	322.2.o.a	160	20
		322.2.o.b	160

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(322))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(322)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)