Space of modular forms of level 1380 and weight 2

• Label: 1380.2
• Level: 1380
• Weight: 2
• Dimension: 19996
• Nonzero newspaces: 24
• Sturm bound: 202752
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(202752\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1380))\).

	Total	New	Old
Modular forms	52448	20508	31940
Cusp forms	48929	19996	28933
Eisenstein series	3519	512	3007

Trace form

19996 * q - 4 * q^3 - 28 * q^4 - 4 * q^5 - 50 * q^6 + 8 * q^7 + 24 * q^8 - 24 * q^9 - 26 * q^10 + 16 * q^11 - 14 * q^12 - 40 * q^13 + 17 * q^15 - 132 * q^16 - 4 * q^17 - 54 * q^18 - 44 * q^19 - 40 * q^20 - 174 * q^21 - 16 * q^22 - 88 * q^23 - 92 * q^24 - 148 * q^25 - 32 * q^26 - 94 * q^27 - 92 * q^28 - 68 * q^29 - 105 * q^30 - 92 * q^31 - 40 * q^32 - 90 * q^33 - 4 * q^34 + 12 * q^35 - 22 * q^36 + 88 * q^37 + 188 * q^38 + 88 * q^39 + 78 * q^40 + 96 * q^41 + 182 * q^42 + 200 * q^43 + 308 * q^44 - 40 * q^45 + 244 * q^46 + 176 * q^47 + 194 * q^48 + 212 * q^49 + 76 * q^50 + 112 * q^51 + 476 * q^52 + 80 * q^53 + 134 * q^54 + 104 * q^55 + 348 * q^56 + 70 * q^57 + 288 * q^58 + 104 * q^59 + 117 * q^60 - 192 * q^61 + 112 * q^62 + 94 * q^63 + 68 * q^64 - 40 * q^65 - 4 * q^66 + 8 * q^67 + 32 * q^68 + 34 * q^69 - 116 * q^70 - 46 * q^72 - 184 * q^73 - 44 * q^74 + 95 * q^75 - 416 * q^76 + 256 * q^77 - 274 * q^78 + 40 * q^79 - 206 * q^80 + 168 * q^81 - 420 * q^82 + 88 * q^83 - 442 * q^84 + 64 * q^85 - 568 * q^86 + 92 * q^87 - 604 * q^88 + 224 * q^89 - 384 * q^90 + 128 * q^91 - 452 * q^92 + 392 * q^93 - 560 * q^94 + 154 * q^95 - 612 * q^96 + 372 * q^97 - 400 * q^98 + 160 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1380))\)

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
1380.2.a	\(\chi_{1380}(1, \cdot)\)	1380.2.a.a	1	1
		1380.2.a.b	1
		1380.2.a.c	1
		1380.2.a.d	1
		1380.2.a.e	1
		1380.2.a.f	2
		1380.2.a.g	2
		1380.2.a.h	2
		1380.2.a.i	2
		1380.2.a.j	3
1380.2.f	\(\chi_{1380}(829, \cdot)\)	1380.2.f.a	6	1
		1380.2.f.b	14
1380.2.g	\(\chi_{1380}(919, \cdot)\)	n/a	144	1
1380.2.h	\(\chi_{1380}(1151, \cdot)\)	n/a	176	1
1380.2.i	\(\chi_{1380}(1241, \cdot)\)	1380.2.i.a	16	1
		1380.2.i.b	16
1380.2.n	\(\chi_{1380}(689, \cdot)\)	1380.2.n.a	48	1
1380.2.o	\(\chi_{1380}(599, \cdot)\)	n/a	264	1
1380.2.p	\(\chi_{1380}(91, \cdot)\)	1380.2.p.a	48	1
		1380.2.p.b	48
1380.2.q	\(\chi_{1380}(827, \cdot)\)	n/a	560	2
1380.2.r	\(\chi_{1380}(737, \cdot)\)	1380.2.r.a	4	2
		1380.2.r.b	4
		1380.2.r.c	80
1380.2.s	\(\chi_{1380}(967, \cdot)\)	n/a	264	2
1380.2.t	\(\chi_{1380}(1057, \cdot)\)	1380.2.t.a	48	2
1380.2.y	\(\chi_{1380}(121, \cdot)\)	n/a	160	10
1380.2.z	\(\chi_{1380}(451, \cdot)\)	n/a	960	10
1380.2.ba	\(\chi_{1380}(59, \cdot)\)	n/a	2800	10
1380.2.bb	\(\chi_{1380}(89, \cdot)\)	n/a	480	10
1380.2.bg	\(\chi_{1380}(221, \cdot)\)	n/a	320	10
1380.2.bh	\(\chi_{1380}(71, \cdot)\)	n/a	1920	10
1380.2.bi	\(\chi_{1380}(19, \cdot)\)	n/a	1440	10
1380.2.bj	\(\chi_{1380}(49, \cdot)\)	n/a	240	10
1380.2.bs	\(\chi_{1380}(37, \cdot)\)	n/a	480	20
1380.2.bt	\(\chi_{1380}(127, \cdot)\)	n/a	2880	20
1380.2.bu	\(\chi_{1380}(77, \cdot)\)	n/a	960	20
1380.2.bv	\(\chi_{1380}(83, \cdot)\)	n/a	5600	20

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1380))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1380)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 2}\)