Space of modular forms of level 1045 and weight 2

• Label: 1045.2
• Level: 1045
• Weight: 2
• Dimension: 37811
• Nonzero newspaces: 36
• Sturm bound: 172800
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(172800\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1045))\).

	Total	New	Old
Modular forms	44640	39643	4997
Cusp forms	41761	37811	3950
Eisenstein series	2879	1832	1047

Trace form

37811 * q - 115 * q^2 - 112 * q^3 - 103 * q^4 - 183 * q^5 - 356 * q^6 - 120 * q^7 - 119 * q^8 - 125 * q^9 - 207 * q^10 - 423 * q^11 - 328 * q^12 - 150 * q^13 - 184 * q^14 - 250 * q^15 - 543 * q^16 - 166 * q^17 - 271 * q^18 - 209 * q^19 - 523 * q^20 - 460 * q^21 - 247 * q^22 - 308 * q^23 - 308 * q^24 - 279 * q^25 - 498 * q^26 - 208 * q^27 - 332 * q^28 - 206 * q^29 - 406 * q^30 - 428 * q^31 - 315 * q^32 - 318 * q^33 - 462 * q^34 - 324 * q^35 - 891 * q^36 - 238 * q^37 - 379 * q^38 - 536 * q^39 - 313 * q^40 - 498 * q^41 - 496 * q^42 - 248 * q^43 - 245 * q^44 - 569 * q^45 - 580 * q^46 - 180 * q^47 - 396 * q^48 - 129 * q^49 - 325 * q^50 - 472 * q^51 - 114 * q^52 - 206 * q^53 - 228 * q^54 - 186 * q^55 - 1080 * q^56 - 228 * q^57 - 162 * q^58 - 204 * q^59 - 418 * q^60 - 470 * q^61 - 492 * q^62 - 328 * q^63 - 495 * q^64 - 372 * q^65 - 778 * q^66 - 592 * q^67 - 590 * q^68 - 512 * q^69 - 592 * q^70 - 688 * q^71 - 563 * q^72 - 498 * q^73 - 602 * q^74 - 420 * q^75 - 759 * q^76 - 622 * q^77 - 668 * q^78 - 488 * q^79 - 355 * q^80 - 649 * q^81 - 562 * q^82 - 248 * q^83 - 152 * q^84 - 270 * q^85 - 544 * q^86 - 224 * q^87 - 401 * q^88 - 382 * q^89 + 147 * q^90 - 464 * q^91 + 28 * q^92 + 148 * q^93 + 148 * q^94 - 107 * q^95 - 220 * q^96 - 26 * q^97 + 81 * q^98 + 15 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1045))\)

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
1045.2.a	\(\chi_{1045}(1, \cdot)\)	1045.2.a.a	1	1
		1045.2.a.b	1
		1045.2.a.c	2
		1045.2.a.d	5
		1045.2.a.e	5
		1045.2.a.f	6
		1045.2.a.g	6
		1045.2.a.h	7
		1045.2.a.i	8
		1045.2.a.j	9
		1045.2.a.k	9
1045.2.b	\(\chi_{1045}(419, \cdot)\)	1045.2.b.a	4	1
		1045.2.b.b	16
		1045.2.b.c	20
		1045.2.b.d	22
		1045.2.b.e	30
1045.2.e	\(\chi_{1045}(1044, \cdot)\)	n/a	116	1
1045.2.f	\(\chi_{1045}(626, \cdot)\)	1045.2.f.a	40	1
		1045.2.f.b	40
1045.2.i	\(\chi_{1045}(771, \cdot)\)	n/a	128	2
1045.2.j	\(\chi_{1045}(153, \cdot)\)	n/a	216	2
1045.2.m	\(\chi_{1045}(683, \cdot)\)	n/a	200	2
1045.2.n	\(\chi_{1045}(191, \cdot)\)	n/a	288	4
1045.2.p	\(\chi_{1045}(791, \cdot)\)	n/a	160	2
1045.2.s	\(\chi_{1045}(164, \cdot)\)	n/a	232	2
1045.2.t	\(\chi_{1045}(144, \cdot)\)	n/a	200	2
1045.2.v	\(\chi_{1045}(111, \cdot)\)	n/a	408	6
1045.2.y	\(\chi_{1045}(151, \cdot)\)	n/a	320	4
1045.2.z	\(\chi_{1045}(94, \cdot)\)	n/a	464	4
1045.2.bc	\(\chi_{1045}(229, \cdot)\)	n/a	432	4
1045.2.bd	\(\chi_{1045}(12, \cdot)\)	n/a	400	4
1045.2.bg	\(\chi_{1045}(87, \cdot)\)	n/a	464	4
1045.2.bh	\(\chi_{1045}(26, \cdot)\)	n/a	640	8
1045.2.bj	\(\chi_{1045}(109, \cdot)\)	n/a	696	6
1045.2.bm	\(\chi_{1045}(21, \cdot)\)	n/a	480	6
1045.2.bo	\(\chi_{1045}(199, \cdot)\)	n/a	600	6
1045.2.bp	\(\chi_{1045}(37, \cdot)\)	n/a	928	8
1045.2.bs	\(\chi_{1045}(172, \cdot)\)	n/a	864	8
1045.2.bu	\(\chi_{1045}(49, \cdot)\)	n/a	928	8
1045.2.bv	\(\chi_{1045}(84, \cdot)\)	n/a	928	8
1045.2.by	\(\chi_{1045}(46, \cdot)\)	n/a	640	8
1045.2.cb	\(\chi_{1045}(43, \cdot)\)	n/a	1392	12
1045.2.cc	\(\chi_{1045}(67, \cdot)\)	n/a	1200	12
1045.2.ce	\(\chi_{1045}(16, \cdot)\)	n/a	1920	24
1045.2.cf	\(\chi_{1045}(7, \cdot)\)	n/a	1856	16
1045.2.ci	\(\chi_{1045}(27, \cdot)\)	n/a	1856	16
1045.2.ck	\(\chi_{1045}(4, \cdot)\)	n/a	2784	24
1045.2.cm	\(\chi_{1045}(41, \cdot)\)	n/a	1920	24
1045.2.cn	\(\chi_{1045}(29, \cdot)\)	n/a	2784	24
1045.2.cr	\(\chi_{1045}(3, \cdot)\)	n/a	5568	48
1045.2.cs	\(\chi_{1045}(17, \cdot)\)	n/a	5568	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1045))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1045)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 2}\)