Space of modular forms of level 323 and weight 2

• Label: 323.2
• Level: 323
• Weight: 2
• Dimension: 4009
• Nonzero newspaces: 15
• Newform subspaces: 34
• Sturm bound: 17280
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 323 = 17 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 15 \)
Newform subspaces:			\( 34 \)
Sturm bound:			\(17280\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(323))\).

	Total	New	Old
Modular forms	4608	4521	87
Cusp forms	4033	4009	24
Eisenstein series	575	512	63

Trace form

4009 * q - 119 * q^2 - 122 * q^3 - 131 * q^4 - 128 * q^5 - 146 * q^6 - 134 * q^7 - 155 * q^8 - 149 * q^9 - 156 * q^10 - 130 * q^11 - 122 * q^12 - 112 * q^13 - 114 * q^14 - 98 * q^15 - 59 * q^16 - 129 * q^17 - 219 * q^18 - 107 * q^19 - 234 * q^20 - 116 * q^21 - 132 * q^22 - 148 * q^23 - 138 * q^24 - 111 * q^25 - 128 * q^26 - 140 * q^27 - 104 * q^28 - 124 * q^29 - 72 * q^30 - 106 * q^31 - 97 * q^32 - 66 * q^33 - 51 * q^34 - 246 * q^35 - 7 * q^36 - 106 * q^37 - 61 * q^38 - 200 * q^39 - 26 * q^40 - 112 * q^41 - 26 * q^42 - 84 * q^43 - 26 * q^44 - 78 * q^45 - 68 * q^46 - 84 * q^47 - 22 * q^48 - 139 * q^49 - 63 * q^50 - 141 * q^51 - 272 * q^52 - 112 * q^53 - 68 * q^54 - 126 * q^55 + 4 * q^56 - 88 * q^57 - 258 * q^58 - 72 * q^59 + 28 * q^60 - 36 * q^61 + 8 * q^62 - 14 * q^63 + 9 * q^64 - 12 * q^65 + 2 * q^66 - 48 * q^67 - 38 * q^68 - 104 * q^69 + 18 * q^70 - 104 * q^71 + 93 * q^72 + 36 * q^73 - 104 * q^74 - 40 * q^75 - 91 * q^76 - 166 * q^77 + 10 * q^78 - 18 * q^79 + 8 * q^80 - 31 * q^81 + 70 * q^82 - 108 * q^83 + 18 * q^84 - 37 * q^85 - 212 * q^86 + 10 * q^87 - 6 * q^88 - 74 * q^89 + 58 * q^90 - 54 * q^91 + 4 * q^92 - 98 * q^93 + 12 * q^94 - 114 * q^95 - 32 * q^96 - 150 * q^97 + 63 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(323))\)

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
323.2.a	\(\chi_{323}(1, \cdot)\)	323.2.a.a	1	1
		323.2.a.b	2
		323.2.a.c	4
		323.2.a.d	5
		323.2.a.e	6
		323.2.a.f	7
323.2.d	\(\chi_{323}(305, \cdot)\)	323.2.d.a	2	1
		323.2.d.b	2
		323.2.d.c	2
		323.2.d.d	10
		323.2.d.e	12
323.2.e	\(\chi_{323}(239, \cdot)\)	323.2.e.a	28	2
		323.2.e.b	28
323.2.f	\(\chi_{323}(115, \cdot)\)	323.2.f.a	2	2
		323.2.f.b	2
		323.2.f.c	2
		323.2.f.d	4
		323.2.f.e	22
		323.2.f.f	24
323.2.h	\(\chi_{323}(220, \cdot)\)	323.2.h.a	56	2
323.2.k	\(\chi_{323}(77, \cdot)\)	323.2.k.a	4	4
		323.2.k.b	40
		323.2.k.c	60
323.2.m	\(\chi_{323}(35, \cdot)\)	323.2.m.a	78	6
		323.2.m.b	78
323.2.o	\(\chi_{323}(30, \cdot)\)	323.2.o.a	112	4
323.2.p	\(\chi_{323}(37, \cdot)\)	323.2.p.a	16	8
		323.2.p.b	208
323.2.s	\(\chi_{323}(16, \cdot)\)	323.2.s.a	168	6
323.2.v	\(\chi_{323}(26, \cdot)\)	323.2.v.a	224	8
323.2.x	\(\chi_{323}(4, \cdot)\)	323.2.x.a	336	12
323.2.y	\(\chi_{323}(12, \cdot)\)	323.2.y.a	448	16
323.2.bb	\(\chi_{323}(9, \cdot)\)	323.2.bb.a	672	24
323.2.bc	\(\chi_{323}(3, \cdot)\)	323.2.bc.a	1344	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(323))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(323)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)