Space of modular forms of level 1445 and weight 4

• Label: 1445.4
• Level: 1445
• Weight: 4
• Dimension: 226201
• Nonzero newspaces: 20
• Sturm bound: 665856
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(665856\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1445))\).

	Total	New	Old
Modular forms	251296	228411	22885
Cusp forms	248096	226201	21895
Eisenstein series	3200	2210	990

Trace form

226201 * q - 244 * q^2 - 238 * q^3 - 232 * q^4 - 365 * q^5 - 728 * q^6 - 234 * q^7 - 240 * q^8 - 263 * q^9 - 548 * q^10 - 1136 * q^11 - 608 * q^12 - 150 * q^13 + 376 * q^14 + 302 * q^15 + 976 * q^16 + 1420 * q^18 + 180 * q^19 - 176 * q^20 - 1092 * q^21 - 1264 * q^22 - 1150 * q^23 - 7728 * q^24 - 2791 * q^25 - 4696 * q^26 - 1204 * q^27 + 384 * q^28 + 750 * q^29 + 2368 * q^30 + 2628 * q^31 + 4720 * q^32 + 4016 * q^33 + 3968 * q^34 + 1258 * q^35 + 5752 * q^36 + 2714 * q^37 - 1952 * q^38 - 5180 * q^39 - 5352 * q^40 - 6378 * q^41 - 12000 * q^42 - 5654 * q^43 - 7792 * q^44 - 2925 * q^45 - 4440 * q^46 + 5326 * q^47 + 12848 * q^48 + 5597 * q^49 + 1124 * q^50 + 2432 * q^51 + 11520 * q^52 - 1470 * q^53 - 10592 * q^54 - 4296 * q^55 - 4720 * q^56 - 8392 * q^57 - 5960 * q^58 - 3196 * q^59 - 3272 * q^60 - 278 * q^61 - 7264 * q^62 + 7494 * q^63 - 5040 * q^64 + 2030 * q^65 + 19728 * q^66 + 8430 * q^67 + 16048 * q^68 + 34324 * q^69 + 34560 * q^70 + 13004 * q^71 + 34544 * q^72 + 15442 * q^73 + 7240 * q^74 + 2954 * q^75 - 4112 * q^76 - 8048 * q^77 - 28576 * q^78 - 14872 * q^79 - 42728 * q^80 - 39883 * q^81 - 44424 * q^82 - 37686 * q^83 - 97968 * q^84 - 20820 * q^85 - 58136 * q^86 - 36244 * q^87 - 48624 * q^88 - 17094 * q^89 - 32292 * q^90 - 11316 * q^91 - 4896 * q^92 + 5432 * q^93 + 20632 * q^94 + 13572 * q^95 + 48336 * q^96 + 19730 * q^97 + 63516 * q^98 + 28912 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1445))\)

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
1445.4.a	\(\chi_{1445}(1, \cdot)\)	1445.4.a.a	1	1
		1445.4.a.b	1
		1445.4.a.c	1
		1445.4.a.d	1
		1445.4.a.e	1
		1445.4.a.f	1
		1445.4.a.g	1
		1445.4.a.h	1
		1445.4.a.i	2
		1445.4.a.j	3
		1445.4.a.k	3
		1445.4.a.l	5
		1445.4.a.m	7
		1445.4.a.n	7
		1445.4.a.o	8
		1445.4.a.p	8
		1445.4.a.q	8
		1445.4.a.r	8
		1445.4.a.s	18
		1445.4.a.t	18
		1445.4.a.u	21
		1445.4.a.v	21
		1445.4.a.w	27
		1445.4.a.x	27
		1445.4.a.y	36
		1445.4.a.z	36
1445.4.b	\(\chi_{1445}(579, \cdot)\)	n/a	392	1
1445.4.c	\(\chi_{1445}(1444, \cdot)\)	n/a	392	1
1445.4.d	\(\chi_{1445}(866, \cdot)\)	n/a	270	1
1445.4.e	\(\chi_{1445}(251, \cdot)\)	n/a	540	2
1445.4.j	\(\chi_{1445}(829, \cdot)\)	n/a	784	2
1445.4.l	\(\chi_{1445}(1001, \cdot)\)	n/a	1080	4
1445.4.m	\(\chi_{1445}(134, \cdot)\)	n/a	1560	4
1445.4.o	\(\chi_{1445}(158, \cdot)\)	n/a	3128	8
1445.4.r	\(\chi_{1445}(447, \cdot)\)	n/a	3128	8
1445.4.s	\(\chi_{1445}(86, \cdot)\)	n/a	4896	16
1445.4.t	\(\chi_{1445}(16, \cdot)\)	n/a	4896	16
1445.4.u	\(\chi_{1445}(84, \cdot)\)	n/a	7296	16
1445.4.v	\(\chi_{1445}(69, \cdot)\)	n/a	7296	16
1445.4.w	\(\chi_{1445}(4, \cdot)\)	n/a	14592	32
1445.4.bb	\(\chi_{1445}(21, \cdot)\)	n/a	9792	32
1445.4.bd	\(\chi_{1445}(9, \cdot)\)	n/a	29312	64
1445.4.be	\(\chi_{1445}(26, \cdot)\)	n/a	19584	64
1445.4.bg	\(\chi_{1445}(12, \cdot)\)	n/a	58496	128
1445.4.bj	\(\chi_{1445}(3, \cdot)\)	n/a	58496	128

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1445))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1445)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)