Space of modular forms of level 841 and weight 2

• Label: 841.2
• Level: 841
• Weight: 2
• Dimension: 28790
• Nonzero newspaces: 8
• Newform subspaces: 51
• Sturm bound: 117740
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 841 = 29^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 51 \)
Sturm bound:			\(117740\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(841))\).

	Total	New	Old
Modular forms	30037	29939	98
Cusp forms	28834	28790	44
Eisenstein series	1203	1149	54

Trace form

28790 * q - 381 * q^2 - 382 * q^3 - 385 * q^4 - 384 * q^5 - 390 * q^6 - 386 * q^7 - 393 * q^8 - 391 * q^9 - 396 * q^10 - 390 * q^11 - 406 * q^12 - 392 * q^13 - 402 * q^14 - 402 * q^15 - 409 * q^16 - 396 * q^17 - 417 * q^18 - 398 * q^19 - 378 * q^20 - 354 * q^21 - 358 * q^22 - 374 * q^23 - 270 * q^24 - 353 * q^25 - 350 * q^26 - 334 * q^27 - 294 * q^28 - 364 * q^29 - 646 * q^30 - 354 * q^31 - 329 * q^32 - 342 * q^33 - 362 * q^34 - 370 * q^35 - 301 * q^36 - 388 * q^37 - 382 * q^38 - 378 * q^39 - 426 * q^40 - 420 * q^41 - 474 * q^42 - 422 * q^43 - 434 * q^44 - 386 * q^45 - 310 * q^46 - 370 * q^47 - 278 * q^48 - 323 * q^49 - 275 * q^50 - 338 * q^51 - 252 * q^52 - 306 * q^53 - 246 * q^54 - 226 * q^55 - 246 * q^56 - 318 * q^57 - 224 * q^58 - 746 * q^59 - 154 * q^60 - 328 * q^61 - 278 * q^62 - 258 * q^63 - 253 * q^64 - 336 * q^65 - 298 * q^66 - 334 * q^67 - 308 * q^68 - 362 * q^69 - 242 * q^70 - 310 * q^71 - 265 * q^72 - 326 * q^73 - 296 * q^74 - 362 * q^75 - 294 * q^76 - 334 * q^77 - 322 * q^78 - 402 * q^79 - 172 * q^80 - 275 * q^81 - 392 * q^82 - 350 * q^83 - 182 * q^84 - 318 * q^85 - 202 * q^86 - 322 * q^87 - 586 * q^88 - 328 * q^89 - 248 * q^90 - 322 * q^91 - 210 * q^92 - 394 * q^93 - 410 * q^94 - 274 * q^95 - 154 * q^96 - 322 * q^97 - 185 * q^98 - 170 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)

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
841.2.a	\(\chi_{841}(1, \cdot)\)	841.2.a.a	2	1
		841.2.a.b	2
		841.2.a.c	2
		841.2.a.d	2
		841.2.a.e	3
		841.2.a.f	3
		841.2.a.g	6
		841.2.a.h	6
		841.2.a.i	8
		841.2.a.j	8
		841.2.a.k	12
841.2.b	\(\chi_{841}(840, \cdot)\)	841.2.b.a	4	1
		841.2.b.b	4
		841.2.b.c	6
		841.2.b.d	12
		841.2.b.e	12
		841.2.b.f	16
841.2.d	\(\chi_{841}(190, \cdot)\)	841.2.d.a	6	6
		841.2.d.b	6
		841.2.d.c	6
		841.2.d.d	6
		841.2.d.e	6
		841.2.d.f	12
		841.2.d.g	12
		841.2.d.h	12
		841.2.d.i	12
		841.2.d.j	12
		841.2.d.k	24
		841.2.d.l	24
		841.2.d.m	24
		841.2.d.n	36
		841.2.d.o	36
		841.2.d.p	48
		841.2.d.q	48
841.2.e	\(\chi_{841}(63, \cdot)\)	841.2.e.a	12	6
		841.2.e.b	12
		841.2.e.c	12
		841.2.e.d	12
		841.2.e.e	12
		841.2.e.f	12
		841.2.e.g	12
		841.2.e.h	12
		841.2.e.i	12
		841.2.e.j	24
		841.2.e.k	24
		841.2.e.l	72
		841.2.e.m	96
841.2.g	\(\chi_{841}(30, \cdot)\)	841.2.g.a	1988	28
841.2.h	\(\chi_{841}(28, \cdot)\)	841.2.h.a	2016	28
841.2.j	\(\chi_{841}(7, \cdot)\)	841.2.j.a	11928	168
841.2.k	\(\chi_{841}(4, \cdot)\)	841.2.k.a	12096	168

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(841))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(841)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)