Space of modular forms of level 380 and weight 3

• Label: 380.3
• Level: 380
• Weight: 3
• Dimension: 4492
• Nonzero newspaces: 18
• Newform subspaces: 20
• Sturm bound: 25920
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 20 \)
Sturm bound:			\(25920\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(380))\).

	Total	New	Old
Modular forms	9000	4700	4300
Cusp forms	8280	4492	3788
Eisenstein series	720	208	512

Trace form

4492 * q - 14 * q^2 - 4 * q^3 - 10 * q^4 - 34 * q^5 - 22 * q^6 + 28 * q^7 - 2 * q^8 - 20 * q^9 - 39 * q^10 - 40 * q^11 - 98 * q^12 - 160 * q^13 - 130 * q^14 - 58 * q^15 - 150 * q^16 - 10 * q^17 - 44 * q^18 + 42 * q^19 + 34 * q^20 + 58 * q^21 + 142 * q^22 + 182 * q^23 + 270 * q^24 - 12 * q^25 + 162 * q^26 + 332 * q^27 + 548 * q^28 + 188 * q^29 + 334 * q^30 + 272 * q^31 + 176 * q^32 + 196 * q^33 - 60 * q^34 - 124 * q^35 - 58 * q^36 - 164 * q^37 - 224 * q^38 - 216 * q^39 - 168 * q^40 - 148 * q^41 - 678 * q^42 - 450 * q^43 - 488 * q^44 - 343 * q^45 - 592 * q^46 - 690 * q^47 - 1404 * q^48 - 426 * q^49 - 550 * q^50 - 710 * q^51 - 130 * q^52 + 128 * q^53 - 404 * q^54 + 84 * q^55 - 324 * q^56 + 70 * q^57 + 36 * q^58 + 270 * q^59 - 458 * q^60 + 1148 * q^61 - 1028 * q^62 + 884 * q^63 - 1474 * q^64 + 391 * q^65 - 1510 * q^66 + 1066 * q^67 - 628 * q^68 + 1450 * q^69 - 407 * q^70 + 562 * q^71 - 684 * q^72 - 334 * q^73 + 318 * q^74 + 124 * q^75 + 126 * q^76 - 470 * q^77 + 610 * q^78 + 204 * q^79 + 621 * q^80 + 588 * q^81 + 1640 * q^82 + 558 * q^83 + 1862 * q^84 + 82 * q^85 + 884 * q^86 + 176 * q^87 + 1534 * q^88 - 222 * q^89 + 1506 * q^90 - 48 * q^91 + 1752 * q^92 - 548 * q^93 + 1540 * q^94 + 503 * q^95 + 2852 * q^96 + 1350 * q^97 + 2748 * q^98 + 1044 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(380))\)

We only show spaces with odd 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
380.3.b	\(\chi_{380}(191, \cdot)\)	380.3.b.a	72	1
380.3.e	\(\chi_{380}(341, \cdot)\)	380.3.e.a	12	1
380.3.g	\(\chi_{380}(189, \cdot)\)	380.3.g.a	4	1
		380.3.g.b	4
		380.3.g.c	12
380.3.h	\(\chi_{380}(39, \cdot)\)	380.3.h.a	108	1
380.3.j	\(\chi_{380}(227, \cdot)\)	380.3.j.a	232	2
380.3.m	\(\chi_{380}(77, \cdot)\)	380.3.m.a	36	2
380.3.o	\(\chi_{380}(69, \cdot)\)	380.3.o.a	40	2
380.3.p	\(\chi_{380}(159, \cdot)\)	380.3.p.a	232	2
380.3.q	\(\chi_{380}(11, \cdot)\)	380.3.q.a	160	2
380.3.t	\(\chi_{380}(141, \cdot)\)	380.3.t.a	24	2
380.3.w	\(\chi_{380}(27, \cdot)\)	380.3.w.a	464	4
380.3.x	\(\chi_{380}(197, \cdot)\)	380.3.x.a	80	4
380.3.z	\(\chi_{380}(21, \cdot)\)	380.3.z.a	84	6
380.3.ba	\(\chi_{380}(99, \cdot)\)	380.3.ba.a	696	6
380.3.bc	\(\chi_{380}(29, \cdot)\)	380.3.bc.a	120	6
380.3.bf	\(\chi_{380}(111, \cdot)\)	380.3.bf.a	480	6
380.3.bg	\(\chi_{380}(17, \cdot)\)	380.3.bg.a	240	12
380.3.bi	\(\chi_{380}(3, \cdot)\)	380.3.bi.a	1392	12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(380))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(380)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 2}\)