Space of modular forms of level 1305 and weight 4

• Label: 1305.4
• Level: 1305
• Weight: 4
• Dimension: 130628
• Nonzero newspaces: 40
• Sturm bound: 483840
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(483840\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1305))\).

	Total	New	Old
Modular forms	183232	132088	51144
Cusp forms	179648	130628	49020
Eisenstein series	3584	1460	2124

Trace form

130628 * q - 80 * q^2 - 108 * q^3 - 144 * q^4 - 138 * q^5 - 268 * q^6 - 36 * q^7 + 60 * q^8 - 44 * q^9 - 554 * q^10 - 500 * q^11 - 464 * q^12 + 148 * q^13 + 612 * q^14 + 238 * q^15 + 944 * q^16 + 1048 * q^17 + 768 * q^18 - 1004 * q^19 - 1138 * q^20 - 1356 * q^21 - 1976 * q^22 - 1756 * q^23 - 1060 * q^24 + 202 * q^25 - 2016 * q^26 - 720 * q^27 + 592 * q^28 - 112 * q^29 + 2576 * q^30 + 1536 * q^31 + 3376 * q^32 + 2920 * q^33 - 820 * q^34 + 1354 * q^35 + 652 * q^36 - 1784 * q^37 + 1400 * q^38 - 132 * q^39 - 2494 * q^40 - 5128 * q^41 - 8848 * q^42 - 2048 * q^43 - 4496 * q^44 - 6022 * q^45 + 7168 * q^46 - 5404 * q^47 - 9668 * q^48 + 370 * q^49 - 4264 * q^50 - 76 * q^51 - 292 * q^52 - 470 * q^53 + 12196 * q^54 - 1406 * q^55 + 752 * q^56 + 5484 * q^57 - 15008 * q^58 + 2552 * q^59 + 5960 * q^60 - 4884 * q^61 - 2560 * q^62 + 4508 * q^63 - 8984 * q^64 + 3397 * q^65 - 2168 * q^66 - 2568 * q^67 + 10948 * q^68 + 3452 * q^69 - 8778 * q^70 - 21348 * q^71 - 30148 * q^72 - 10790 * q^73 - 27104 * q^74 + 1742 * q^75 - 9464 * q^76 + 6024 * q^77 + 14328 * q^78 + 12288 * q^79 + 32450 * q^80 + 22900 * q^81 + 42124 * q^82 + 17436 * q^83 + 34520 * q^84 + 25546 * q^85 + 45484 * q^86 + 12858 * q^87 + 63660 * q^88 + 360 * q^89 - 22752 * q^90 + 9084 * q^91 + 22644 * q^92 - 9804 * q^93 + 7764 * q^94 + 922 * q^95 - 12528 * q^96 + 17406 * q^97 - 6384 * q^98 - 19444 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1305))\)

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
1305.4.a	\(\chi_{1305}(1, \cdot)\)	1305.4.a.a	1	1
		1305.4.a.b	1
		1305.4.a.c	1
		1305.4.a.d	1
		1305.4.a.e	2
		1305.4.a.f	2
		1305.4.a.g	5
		1305.4.a.h	6
		1305.4.a.i	6
		1305.4.a.j	6
		1305.4.a.k	6
		1305.4.a.l	7
		1305.4.a.m	7
		1305.4.a.n	7
		1305.4.a.o	8
		1305.4.a.p	8
		1305.4.a.q	10
		1305.4.a.r	12
		1305.4.a.s	12
		1305.4.a.t	16
		1305.4.a.u	16
1305.4.c	\(\chi_{1305}(784, \cdot)\)	n/a	210	1
1305.4.d	\(\chi_{1305}(811, \cdot)\)	n/a	150	1
1305.4.f	\(\chi_{1305}(289, \cdot)\)	n/a	224	1
1305.4.i	\(\chi_{1305}(436, \cdot)\)	n/a	672	2
1305.4.k	\(\chi_{1305}(568, \cdot)\)	n/a	446	2
1305.4.m	\(\chi_{1305}(539, \cdot)\)	n/a	360	2
1305.4.n	\(\chi_{1305}(233, \cdot)\)	n/a	336	2
1305.4.q	\(\chi_{1305}(782, \cdot)\)	n/a	360	2
1305.4.r	\(\chi_{1305}(476, \cdot)\)	n/a	240	2
1305.4.t	\(\chi_{1305}(307, \cdot)\)	n/a	446	2
1305.4.w	\(\chi_{1305}(724, \cdot)\)	n/a	1072	2
1305.4.y	\(\chi_{1305}(376, \cdot)\)	n/a	720	2
1305.4.bb	\(\chi_{1305}(349, \cdot)\)	n/a	1008	2
1305.4.bc	\(\chi_{1305}(136, \cdot)\)	n/a	900	6
1305.4.bd	\(\chi_{1305}(418, \cdot)\)	n/a	2144	4
1305.4.bg	\(\chi_{1305}(41, \cdot)\)	n/a	1440	4
1305.4.bi	\(\chi_{1305}(173, \cdot)\)	n/a	2144	4
1305.4.bj	\(\chi_{1305}(407, \cdot)\)	n/a	2016	4
1305.4.bl	\(\chi_{1305}(104, \cdot)\)	n/a	2144	4
1305.4.bo	\(\chi_{1305}(133, \cdot)\)	n/a	2144	4
1305.4.br	\(\chi_{1305}(64, \cdot)\)	n/a	1344	6
1305.4.bt	\(\chi_{1305}(91, \cdot)\)	n/a	900	6
1305.4.bu	\(\chi_{1305}(199, \cdot)\)	n/a	1332	6
1305.4.bw	\(\chi_{1305}(16, \cdot)\)	n/a	4320	12
1305.4.by	\(\chi_{1305}(73, \cdot)\)	n/a	2676	12
1305.4.ca	\(\chi_{1305}(26, \cdot)\)	n/a	1440	12
1305.4.cb	\(\chi_{1305}(62, \cdot)\)	n/a	2160	12
1305.4.ce	\(\chi_{1305}(53, \cdot)\)	n/a	2160	12
1305.4.cf	\(\chi_{1305}(44, \cdot)\)	n/a	2160	12
1305.4.ch	\(\chi_{1305}(37, \cdot)\)	n/a	2676	12
1305.4.cj	\(\chi_{1305}(49, \cdot)\)	n/a	6432	12
1305.4.cm	\(\chi_{1305}(121, \cdot)\)	n/a	4320	12
1305.4.co	\(\chi_{1305}(4, \cdot)\)	n/a	6432	12
1305.4.cq	\(\chi_{1305}(43, \cdot)\)	n/a	12864	24
1305.4.ct	\(\chi_{1305}(14, \cdot)\)	n/a	12864	24
1305.4.cv	\(\chi_{1305}(23, \cdot)\)	n/a	12864	24
1305.4.cw	\(\chi_{1305}(38, \cdot)\)	n/a	12864	24
1305.4.cy	\(\chi_{1305}(11, \cdot)\)	n/a	8640	24
1305.4.db	\(\chi_{1305}(292, \cdot)\)	n/a	12864	24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1305))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1305)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 2}\)