Space of modular forms of level 396 and weight 2

• Label: 396.2
• Level: 396
• Weight: 2
• Dimension: 1879
• Nonzero newspaces: 16
• Newform subspaces: 39
• Sturm bound: 17280
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 39 \)
Sturm bound:			\(17280\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(396))\).

	Total	New	Old
Modular forms	4720	2043	2677
Cusp forms	3921	1879	2042
Eisenstein series	799	164	635

Trace form

1879 * q - 9 * q^2 - 5 * q^4 - 12 * q^5 - 14 * q^6 + q^7 - 15 * q^8 - 16 * q^9 - 32 * q^10 - 2 * q^11 - 52 * q^12 - 21 * q^13 - 34 * q^14 - 18 * q^15 - 9 * q^16 - 49 * q^17 - 56 * q^18 + 15 * q^19 - 26 * q^20 - 34 * q^21 + 12 * q^22 + 19 * q^23 - 26 * q^24 + 38 * q^25 + 10 * q^26 + 30 * q^27 + 4 * q^28 + 19 * q^29 + 16 * q^30 + 58 * q^31 + 36 * q^32 - 5 * q^33 - 24 * q^34 + 97 * q^35 + 46 * q^36 + 14 * q^38 + 36 * q^39 - 54 * q^40 + 3 * q^41 - 4 * q^42 + 12 * q^43 - 50 * q^44 - 100 * q^45 - 94 * q^46 - 23 * q^47 - 62 * q^48 - 63 * q^49 - 167 * q^50 - 10 * q^51 - 164 * q^52 - 41 * q^53 - 178 * q^54 - 88 * q^55 - 236 * q^56 - 132 * q^57 - 204 * q^58 - 126 * q^59 - 172 * q^60 - 125 * q^61 - 240 * q^62 - 74 * q^63 - 245 * q^64 - 156 * q^65 - 126 * q^66 - 127 * q^67 - 180 * q^68 - 42 * q^69 - 218 * q^70 - 92 * q^71 - 128 * q^72 - 59 * q^73 - 190 * q^74 - 46 * q^75 - 164 * q^76 - 148 * q^77 - 116 * q^78 - 45 * q^79 - 190 * q^80 - 96 * q^81 - 183 * q^82 - 93 * q^83 - 150 * q^84 - 75 * q^85 - 67 * q^86 - 82 * q^87 - 74 * q^88 - 179 * q^89 - 32 * q^90 + 97 * q^91 - 138 * q^92 - 230 * q^93 - 4 * q^94 - 129 * q^95 - 14 * q^96 - 46 * q^97 - 169 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)

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
396.2.a	\(\chi_{396}(1, \cdot)\)	396.2.a.a	1	1
		396.2.a.b	1
		396.2.a.c	1
396.2.b	\(\chi_{396}(197, \cdot)\)	396.2.b.a	2	1
		396.2.b.b	2
396.2.c	\(\chi_{396}(287, \cdot)\)	396.2.c.a	10	1
		396.2.c.b	10
396.2.h	\(\chi_{396}(307, \cdot)\)	396.2.h.a	4	1
		396.2.h.b	4
		396.2.h.c	8
		396.2.h.d	12
396.2.i	\(\chi_{396}(133, \cdot)\)	396.2.i.a	2	2
		396.2.i.b	2
		396.2.i.c	2
		396.2.i.d	6
		396.2.i.e	8
396.2.j	\(\chi_{396}(37, \cdot)\)	396.2.j.a	4	4
		396.2.j.b	4
		396.2.j.c	4
		396.2.j.d	8
396.2.k	\(\chi_{396}(43, \cdot)\)	396.2.k.a	4	2
		396.2.k.b	4
		396.2.k.c	4
		396.2.k.d	4
		396.2.k.e	120
396.2.p	\(\chi_{396}(23, \cdot)\)	396.2.p.a	60	2
		396.2.p.b	60
396.2.q	\(\chi_{396}(65, \cdot)\)	396.2.q.a	4	2
		396.2.q.b	4
		396.2.q.c	16
396.2.r	\(\chi_{396}(19, \cdot)\)	396.2.r.a	16	4
		396.2.r.b	48
		396.2.r.c	48
396.2.w	\(\chi_{396}(71, \cdot)\)	396.2.w.a	96	4
396.2.x	\(\chi_{396}(17, \cdot)\)	396.2.x.a	16	4
396.2.y	\(\chi_{396}(25, \cdot)\)	396.2.y.a	96	8
396.2.z	\(\chi_{396}(29, \cdot)\)	396.2.z.a	96	8
396.2.ba	\(\chi_{396}(47, \cdot)\)	396.2.ba.a	544	8
396.2.bf	\(\chi_{396}(7, \cdot)\)	396.2.bf.a	544	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(396))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(396)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)