Space of modular forms of level 1805 and weight 2

• Label: 1805.2
• Level: 1805
• Weight: 2
• Dimension: 117067
• Nonzero newspaces: 18
• Sturm bound: 519840
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(519840\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1805))\).

	Total	New	Old
Modular forms	131976	119877	12099
Cusp forms	127945	117067	10878
Eisenstein series	4031	2810	1221

Trace form

117067 * q - 303 * q^2 - 302 * q^3 - 299 * q^4 - 458 * q^5 - 906 * q^6 - 298 * q^7 - 291 * q^8 - 293 * q^9 - 456 * q^10 - 906 * q^11 - 326 * q^12 - 340 * q^13 - 354 * q^14 - 491 * q^15 - 1031 * q^16 - 324 * q^17 - 411 * q^18 - 366 * q^19 - 956 * q^20 - 970 * q^21 - 378 * q^22 - 318 * q^23 - 390 * q^24 - 494 * q^25 - 948 * q^26 - 350 * q^27 - 406 * q^28 - 348 * q^29 - 573 * q^30 - 958 * q^31 - 423 * q^32 - 474 * q^33 - 432 * q^34 - 523 * q^35 - 1259 * q^36 - 376 * q^37 - 450 * q^38 - 754 * q^39 - 606 * q^40 - 948 * q^41 - 570 * q^42 - 418 * q^43 - 510 * q^44 - 608 * q^45 - 1170 * q^46 - 438 * q^47 - 686 * q^48 - 405 * q^49 - 654 * q^50 - 1062 * q^51 - 472 * q^52 - 396 * q^53 - 510 * q^54 - 519 * q^55 - 1266 * q^56 - 414 * q^57 - 648 * q^58 - 426 * q^59 - 737 * q^60 - 1120 * q^61 - 606 * q^62 - 538 * q^63 - 731 * q^64 - 643 * q^65 - 1350 * q^66 - 610 * q^67 - 684 * q^68 - 606 * q^69 - 723 * q^70 - 1098 * q^71 - 615 * q^72 - 568 * q^73 - 552 * q^74 - 521 * q^75 - 1152 * q^76 - 822 * q^77 - 426 * q^78 - 490 * q^79 - 320 * q^80 - 977 * q^81 - 576 * q^82 - 258 * q^83 - 82 * q^84 - 369 * q^85 - 894 * q^86 - 186 * q^87 - 54 * q^88 - 324 * q^89 - 114 * q^90 - 854 * q^91 - 30 * q^92 - 10 * q^93 + 18 * q^94 - 441 * q^95 - 1242 * q^96 - 244 * q^97 - 243 * q^98 - 114 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1805))\)

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
1805.2.a	\(\chi_{1805}(1, \cdot)\)	1805.2.a.a	1	1
		1805.2.a.b	1
		1805.2.a.c	2
		1805.2.a.d	2
		1805.2.a.e	2
		1805.2.a.f	3
		1805.2.a.g	3
		1805.2.a.h	3
		1805.2.a.i	4
		1805.2.a.j	4
		1805.2.a.k	4
		1805.2.a.l	4
		1805.2.a.m	4
		1805.2.a.n	4
		1805.2.a.o	4
		1805.2.a.p	4
		1805.2.a.q	6
		1805.2.a.r	6
		1805.2.a.s	9
		1805.2.a.t	9
		1805.2.a.u	9
		1805.2.a.v	9
		1805.2.a.w	16
1805.2.b	\(\chi_{1805}(1084, \cdot)\)	1805.2.b.a	2	1
		1805.2.b.b	2
		1805.2.b.c	2
		1805.2.b.d	2
		1805.2.b.e	6
		1805.2.b.f	6
		1805.2.b.g	6
		1805.2.b.h	8
		1805.2.b.i	16
		1805.2.b.j	16
		1805.2.b.k	24
		1805.2.b.l	24
		1805.2.b.m	40
1805.2.e	\(\chi_{1805}(1151, \cdot)\)	n/a	224	2
1805.2.g	\(\chi_{1805}(1082, \cdot)\)	n/a	308	2
1805.2.i	\(\chi_{1805}(429, \cdot)\)	n/a	308	2
1805.2.k	\(\chi_{1805}(606, \cdot)\)	n/a	684	6
1805.2.l	\(\chi_{1805}(293, \cdot)\)	n/a	616	4
1805.2.p	\(\chi_{1805}(54, \cdot)\)	n/a	924	6
1805.2.q	\(\chi_{1805}(96, \cdot)\)	n/a	2304	18
1805.2.s	\(\chi_{1805}(127, \cdot)\)	n/a	1848	12
1805.2.v	\(\chi_{1805}(39, \cdot)\)	n/a	3384	18
1805.2.w	\(\chi_{1805}(11, \cdot)\)	n/a	4608	36
1805.2.x	\(\chi_{1805}(18, \cdot)\)	n/a	6768	36
1805.2.ba	\(\chi_{1805}(49, \cdot)\)	n/a	6768	36
1805.2.bc	\(\chi_{1805}(6, \cdot)\)	n/a	13608	108
1805.2.be	\(\chi_{1805}(8, \cdot)\)	n/a	13536	72
1805.2.bf	\(\chi_{1805}(4, \cdot)\)	n/a	20304	108
1805.2.bi	\(\chi_{1805}(2, \cdot)\)	n/a	40608	216

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1805))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1805)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1805))\)\(^{\oplus 1}\)