Space of modular forms of level 1183 and weight 2

• Label: 1183.2
• Level: 1183
• Weight: 2
• Dimension: 52755
• Nonzero newspaces: 30
• Sturm bound: 227136
• Trace bound: 3

Defining parameters

Level:	$N$	=	$1183 = 7 \cdot 13^{2}$
Weight:	$k$	=	$2$
Nonzero newspaces:			$30$
Sturm bound:			$227136$
Trace bound:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(1183))$.

	Total	New	Old
Modular forms	58152	54799	3353
Cusp forms	55417	52755	2662
Eisenstein series	2735	2044	691

Trace form

52755 * q - 261 * q^2 - 260 * q^3 - 257 * q^4 - 258 * q^5 - 252 * q^6 - 333 * q^7 - 681 * q^8 - 283 * q^9 - 306 * q^10 - 276 * q^11 - 340 * q^12 - 312 * q^13 - 651 * q^14 - 684 * q^15 - 313 * q^16 - 282 * q^17 - 357 * q^18 - 324 * q^19 - 354 * q^20 - 378 * q^21 - 744 * q^22 - 288 * q^23 - 444 * q^24 - 317 * q^25 - 348 * q^26 - 608 * q^27 - 423 * q^28 - 738 * q^29 - 480 * q^30 - 336 * q^31 - 465 * q^32 - 384 * q^33 - 402 * q^34 - 408 * q^35 - 905 * q^36 - 294 * q^37 - 372 * q^38 - 352 * q^39 - 702 * q^40 - 402 * q^41 - 498 * q^42 - 800 * q^43 - 492 * q^44 - 486 * q^45 - 528 * q^46 - 384 * q^47 - 572 * q^48 - 445 * q^49 - 939 * q^50 - 504 * q^51 - 454 * q^52 - 642 * q^53 - 552 * q^54 - 456 * q^55 - 543 * q^56 - 876 * q^57 - 474 * q^58 - 372 * q^59 - 744 * q^60 - 430 * q^61 - 504 * q^62 - 513 * q^63 - 1025 * q^64 - 450 * q^65 - 888 * q^66 - 420 * q^67 - 630 * q^68 - 480 * q^69 - 588 * q^70 - 828 * q^71 - 381 * q^72 - 438 * q^73 - 498 * q^74 - 460 * q^75 - 300 * q^76 - 282 * q^77 - 924 * q^78 - 376 * q^79 - 282 * q^80 - 247 * q^81 - 6 * q^82 - 276 * q^83 - 66 * q^84 - 492 * q^85 - 348 * q^86 - 192 * q^87 + 84 * q^88 - 270 * q^89 - 126 * q^90 - 302 * q^91 - 1092 * q^92 - 360 * q^93 + 24 * q^94 - 288 * q^95 - 132 * q^96 - 54 * q^97 - 243 * q^98 - 672 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(1183))$

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
1183.2.a	$\chi_{1183}(1, \cdot)$	1183.2.a.a	1	1
		1183.2.a.b	1
		1183.2.a.c	2
		1183.2.a.d	2
		1183.2.a.e	2
		1183.2.a.f	2
		1183.2.a.g	2
		1183.2.a.h	3
		1183.2.a.i	3
		1183.2.a.j	3
		1183.2.a.k	4
		1183.2.a.l	4
		1183.2.a.m	6
		1183.2.a.n	6
		1183.2.a.o	6
		1183.2.a.p	6
		1183.2.a.q	12
		1183.2.a.r	12
1183.2.c	$\chi_{1183}(337, \cdot)$	1183.2.c.a	2	1
		1183.2.c.b	2
		1183.2.c.c	4
		1183.2.c.d	4
		1183.2.c.e	4
		1183.2.c.f	6
		1183.2.c.g	8
		1183.2.c.h	12
		1183.2.c.i	12
		1183.2.c.j	24
1183.2.e	$\chi_{1183}(170, \cdot)$	1183.2.e.a	2	2
		1183.2.e.b	2
		1183.2.e.c	2
		1183.2.e.d	4
		1183.2.e.e	4
		1183.2.e.f	10
		1183.2.e.g	12
		1183.2.e.h	12
		1183.2.e.i	16
		1183.2.e.j	24
		1183.2.e.k	48
		1183.2.e.l	48
1183.2.f	$\chi_{1183}(22, \cdot)$	n/a	152	2
1183.2.g	$\chi_{1183}(191, \cdot)$	n/a	186	2
1183.2.h	$\chi_{1183}(529, \cdot)$	n/a	186	2
1183.2.i	$\chi_{1183}(944, \cdot)$	n/a	188	2
1183.2.k	$\chi_{1183}(23, \cdot)$	n/a	186	2
1183.2.q	$\chi_{1183}(316, \cdot)$	n/a	156	2
1183.2.r	$\chi_{1183}(506, \cdot)$	n/a	184	2
1183.2.u	$\chi_{1183}(361, \cdot)$	n/a	186	2
1183.2.w	$\chi_{1183}(19, \cdot)$	n/a	372	4
1183.2.ba	$\chi_{1183}(89, \cdot)$	n/a	372	4
1183.2.bb	$\chi_{1183}(437, \cdot)$	n/a	368	4
1183.2.bc	$\chi_{1183}(188, \cdot)$	n/a	368	4
1183.2.be	$\chi_{1183}(92, \cdot)$	n/a	1104	12
1183.2.bg	$\chi_{1183}(64, \cdot)$	n/a	1080	12
1183.2.bi	$\chi_{1183}(16, \cdot)$	n/a	2856	24
1183.2.bj	$\chi_{1183}(9, \cdot)$	n/a	2856	24
1183.2.bk	$\chi_{1183}(29, \cdot)$	n/a	2208	24
1183.2.bl	$\chi_{1183}(53, \cdot)$	n/a	2880	24
1183.2.bn	$\chi_{1183}(34, \cdot)$	n/a	2832	24
1183.2.bp	$\chi_{1183}(30, \cdot)$	n/a	2856	24
1183.2.bs	$\chi_{1183}(25, \cdot)$	n/a	2880	24
1183.2.bt	$\chi_{1183}(36, \cdot)$	n/a	2160	24
1183.2.bz	$\chi_{1183}(4, \cdot)$	n/a	2856	24
1183.2.cb	$\chi_{1183}(6, \cdot)$	n/a	5760	48
1183.2.cc	$\chi_{1183}(5, \cdot)$	n/a	5760	48
1183.2.cd	$\chi_{1183}(45, \cdot)$	n/a	5712	48
1183.2.ch	$\chi_{1183}(24, \cdot)$	n/a	5712	48

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(1183))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(1183)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$^{\oplus 2}$