Space of modular forms of level 961 and weight 2

• Label: 961.2
• Level: 961
• Weight: 2
• Dimension: 37699
• Nonzero newspaces: 8
• Newform subspaces: 70
• Sturm bound: 153760
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 961 = 31^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 70 \)
Sturm bound:			\(153760\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(961))\).

	Total	New	Old
Modular forms	39130	39020	110
Cusp forms	37751	37699	52
Eisenstein series	1379	1321	58

Trace form

37699 * q - 438 * q^2 - 439 * q^3 - 442 * q^4 - 441 * q^5 - 447 * q^6 - 443 * q^7 - 450 * q^8 - 448 * q^9 - 453 * q^10 - 447 * q^11 - 463 * q^12 - 449 * q^13 - 459 * q^14 - 459 * q^15 - 466 * q^16 - 453 * q^17 - 474 * q^18 - 455 * q^19 - 477 * q^20 - 457 * q^21 - 411 * q^22 - 429 * q^23 - 375 * q^24 - 396 * q^25 - 417 * q^26 - 385 * q^27 - 331 * q^28 - 405 * q^29 - 357 * q^30 - 420 * q^31 - 738 * q^32 - 423 * q^33 - 369 * q^34 - 423 * q^35 - 366 * q^36 - 383 * q^37 - 435 * q^38 - 421 * q^39 - 405 * q^40 - 447 * q^41 - 471 * q^42 - 469 * q^43 - 519 * q^44 - 513 * q^45 - 507 * q^46 - 483 * q^47 - 469 * q^48 - 432 * q^49 - 378 * q^50 - 327 * q^51 - 383 * q^52 - 429 * q^53 - 225 * q^54 - 387 * q^55 - 285 * q^56 - 335 * q^57 - 315 * q^58 - 435 * q^59 - 93 * q^60 - 287 * q^61 - 360 * q^62 - 719 * q^63 - 322 * q^64 - 339 * q^65 - 129 * q^66 - 443 * q^67 - 351 * q^68 - 351 * q^69 - 309 * q^70 - 387 * q^71 - 300 * q^72 - 449 * q^73 - 399 * q^74 - 349 * q^75 - 325 * q^76 - 381 * q^77 - 333 * q^78 - 445 * q^79 - 321 * q^80 - 436 * q^81 - 441 * q^82 - 309 * q^83 - 299 * q^84 - 423 * q^85 - 327 * q^86 - 435 * q^87 - 255 * q^88 - 375 * q^89 - 219 * q^90 - 417 * q^91 - 213 * q^92 - 330 * q^93 - 879 * q^94 - 315 * q^95 - 237 * q^96 - 403 * q^97 - 246 * q^98 - 441 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(961))\)

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
961.2.a	\(\chi_{961}(1, \cdot)\)	961.2.a.a	2	1
		961.2.a.b	2
		961.2.a.c	2
		961.2.a.d	2
		961.2.a.e	2
		961.2.a.f	2
		961.2.a.g	3
		961.2.a.h	4
		961.2.a.i	8
		961.2.a.j	8
		961.2.a.k	12
		961.2.a.l	16
961.2.c	\(\chi_{961}(439, \cdot)\)	961.2.c.a	4	2
		961.2.c.b	4
		961.2.c.c	4
		961.2.c.d	4
		961.2.c.e	4
		961.2.c.f	4
		961.2.c.g	6
		961.2.c.h	8
		961.2.c.i	16
		961.2.c.j	16
		961.2.c.k	24
		961.2.c.l	32
961.2.d	\(\chi_{961}(374, \cdot)\)	961.2.d.a	4	4
		961.2.d.b	4
		961.2.d.c	4
		961.2.d.d	4
		961.2.d.e	4
		961.2.d.f	4
		961.2.d.g	4
		961.2.d.h	8
		961.2.d.i	8
		961.2.d.j	8
		961.2.d.k	8
		961.2.d.l	8
		961.2.d.m	12
		961.2.d.n	16
		961.2.d.o	16
		961.2.d.p	16
		961.2.d.q	16
		961.2.d.r	48
		961.2.d.s	64
961.2.g	\(\chi_{961}(235, \cdot)\)	961.2.g.a	8	8
		961.2.g.b	8
		961.2.g.c	8
		961.2.g.d	8
		961.2.g.e	8
		961.2.g.f	8
		961.2.g.g	8
		961.2.g.h	8
		961.2.g.i	16
		961.2.g.j	16
		961.2.g.k	16
		961.2.g.l	16
		961.2.g.m	16
		961.2.g.n	16
		961.2.g.o	16
		961.2.g.p	16
		961.2.g.q	16
		961.2.g.r	16
		961.2.g.s	16
		961.2.g.t	16
		961.2.g.u	24
		961.2.g.v	96
		961.2.g.w	128
961.2.i	\(\chi_{961}(32, \cdot)\)	961.2.i.a	2430	30
961.2.k	\(\chi_{961}(5, \cdot)\)	961.2.k.a	4920	60
961.2.l	\(\chi_{961}(2, \cdot)\)	961.2.l.a	9720	120
961.2.o	\(\chi_{961}(7, \cdot)\)	961.2.o.a	19680	240

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(961))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(961)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(961))\)\(^{\oplus 1}\)