Space of modular forms of level 1445 and weight 2

• Label: 1445.2
• Level: 1445
• Weight: 2
• Dimension: 74665
• Nonzero newspaces: 20
• Sturm bound: 332928
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(332928\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1445))\).

	Total	New	Old
Modular forms	84832	76875	7957
Cusp forms	81633	74665	6968
Eisenstein series	3199	2210	989

Trace form

74665 * q - 237 * q^2 - 236 * q^3 - 233 * q^4 - 359 * q^5 - 708 * q^6 - 232 * q^7 - 225 * q^8 - 227 * q^9 - 365 * q^10 - 740 * q^11 - 308 * q^12 - 258 * q^13 - 280 * q^14 - 404 * q^15 - 833 * q^16 - 272 * q^17 - 553 * q^18 - 252 * q^19 - 409 * q^20 - 784 * q^21 - 268 * q^22 - 248 * q^23 - 340 * q^24 - 415 * q^25 - 822 * q^26 - 296 * q^27 - 376 * q^28 - 290 * q^29 - 476 * q^30 - 816 * q^31 - 401 * q^32 - 352 * q^33 - 384 * q^34 - 752 * q^35 - 949 * q^36 - 330 * q^37 - 372 * q^38 - 376 * q^39 - 537 * q^40 - 854 * q^41 - 528 * q^42 - 356 * q^43 - 540 * q^44 - 451 * q^45 - 840 * q^46 - 352 * q^47 - 532 * q^48 - 311 * q^49 - 405 * q^50 - 832 * q^51 - 622 * q^52 - 362 * q^53 - 600 * q^54 - 476 * q^55 - 1080 * q^56 - 544 * q^57 - 502 * q^58 - 436 * q^59 - 668 * q^60 - 914 * q^61 - 560 * q^62 - 616 * q^63 - 305 * q^64 - 498 * q^65 - 1088 * q^66 - 332 * q^67 - 408 * q^68 - 688 * q^69 - 352 * q^70 - 712 * q^71 - 349 * q^72 - 246 * q^73 - 174 * q^74 - 356 * q^75 - 548 * q^76 - 208 * q^77 - 232 * q^78 - 160 * q^79 - 41 * q^80 - 631 * q^81 - 2 * q^82 - 220 * q^83 + 80 * q^84 - 284 * q^85 - 1452 * q^86 - 120 * q^87 + 68 * q^88 - 246 * q^89 - 233 * q^90 - 672 * q^91 - 200 * q^92 - 240 * q^93 - 224 * q^94 - 308 * q^95 - 1012 * q^96 - 142 * q^97 - 469 * q^98 - 372 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)

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
1445.2.a	\(\chi_{1445}(1, \cdot)\)	1445.2.a.a	1	1
		1445.2.a.b	1
		1445.2.a.c	1
		1445.2.a.d	1
		1445.2.a.e	1
		1445.2.a.f	2
		1445.2.a.g	2
		1445.2.a.h	2
		1445.2.a.i	2
		1445.2.a.j	3
		1445.2.a.k	3
		1445.2.a.l	6
		1445.2.a.m	6
		1445.2.a.n	6
		1445.2.a.o	6
		1445.2.a.p	12
		1445.2.a.q	12
		1445.2.a.r	12
		1445.2.a.s	12
1445.2.b	\(\chi_{1445}(579, \cdot)\)	1445.2.b.a	4	1
		1445.2.b.b	8
		1445.2.b.c	8
		1445.2.b.d	8
		1445.2.b.e	8
		1445.2.b.f	12
		1445.2.b.g	24
		1445.2.b.h	24
		1445.2.b.i	24
1445.2.c	\(\chi_{1445}(1444, \cdot)\)	n/a	120	1
1445.2.d	\(\chi_{1445}(866, \cdot)\)	1445.2.d.a	2	1
		1445.2.d.b	2
		1445.2.d.c	2
		1445.2.d.d	4
		1445.2.d.e	4
		1445.2.d.f	4
		1445.2.d.g	12
		1445.2.d.h	12
		1445.2.d.i	24
		1445.2.d.j	24
1445.2.e	\(\chi_{1445}(251, \cdot)\)	n/a	180	2
1445.2.j	\(\chi_{1445}(829, \cdot)\)	n/a	240	2
1445.2.l	\(\chi_{1445}(1001, \cdot)\)	n/a	360	4
1445.2.m	\(\chi_{1445}(134, \cdot)\)	n/a	488	4
1445.2.o	\(\chi_{1445}(158, \cdot)\)	n/a	968	8
1445.2.r	\(\chi_{1445}(447, \cdot)\)	n/a	968	8
1445.2.s	\(\chi_{1445}(86, \cdot)\)	n/a	1632	16
1445.2.t	\(\chi_{1445}(16, \cdot)\)	n/a	1632	16
1445.2.u	\(\chi_{1445}(84, \cdot)\)	n/a	2432	16
1445.2.v	\(\chi_{1445}(69, \cdot)\)	n/a	2432	16
1445.2.w	\(\chi_{1445}(4, \cdot)\)	n/a	4864	32
1445.2.bb	\(\chi_{1445}(21, \cdot)\)	n/a	3264	32
1445.2.bd	\(\chi_{1445}(9, \cdot)\)	n/a	9600	64
1445.2.be	\(\chi_{1445}(26, \cdot)\)	n/a	6528	64
1445.2.bg	\(\chi_{1445}(12, \cdot)\)	n/a	19328	128
1445.2.bj	\(\chi_{1445}(3, \cdot)\)	n/a	19328	128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1445))\) into lower level spaces

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