Space of modular forms of level 693 and weight 4

• Label: 693.4
• Level: 693
• Weight: 4
• Dimension: 38270
• Nonzero newspaces: 40
• Sturm bound: 138240
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(138240\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(693))\).

	Total	New	Old
Modular forms	52800	39082	13718
Cusp forms	50880	38270	12610
Eisenstein series	1920	812	1108

Trace form

38270 * q - 54 * q^2 - 68 * q^3 - 94 * q^4 - 126 * q^5 - 20 * q^6 - 69 * q^7 + 124 * q^8 + 124 * q^9 - 214 * q^10 - 283 * q^11 - 856 * q^12 - 612 * q^13 - 1086 * q^14 - 284 * q^15 + 882 * q^16 + 1470 * q^17 + 1480 * q^18 + 352 * q^19 + 2002 * q^20 + 686 * q^21 - 456 * q^22 - 1766 * q^23 - 2276 * q^24 - 2278 * q^25 - 4562 * q^26 - 2456 * q^27 - 1486 * q^28 + 70 * q^29 + 1036 * q^30 + 430 * q^31 + 3340 * q^32 + 2784 * q^33 + 2300 * q^34 + 2461 * q^35 + 3068 * q^36 + 3534 * q^37 + 8842 * q^38 + 4900 * q^39 + 1398 * q^40 - 312 * q^41 + 1964 * q^42 - 3404 * q^43 - 6260 * q^44 - 2532 * q^45 + 466 * q^46 - 838 * q^47 + 3644 * q^48 - 3361 * q^49 - 5648 * q^50 - 256 * q^51 - 24430 * q^52 - 16342 * q^53 - 11472 * q^54 - 4690 * q^55 - 12918 * q^56 - 9228 * q^57 + 5714 * q^58 - 4260 * q^59 - 7620 * q^60 + 6234 * q^61 + 12342 * q^62 - 4566 * q^63 + 15004 * q^64 + 4386 * q^65 + 8594 * q^66 + 8198 * q^67 + 2834 * q^68 + 444 * q^69 - 1456 * q^70 + 16326 * q^71 + 10660 * q^72 + 5410 * q^73 + 7170 * q^74 + 7856 * q^75 + 9676 * q^76 + 6783 * q^77 + 3480 * q^78 + 4186 * q^79 + 26118 * q^80 + 13252 * q^81 - 3232 * q^82 + 19706 * q^83 + 31034 * q^84 + 7766 * q^85 + 24688 * q^86 + 9084 * q^87 - 27408 * q^88 - 13406 * q^89 - 14308 * q^90 - 14805 * q^91 - 40556 * q^92 - 17868 * q^93 - 15378 * q^94 - 31758 * q^95 - 62140 * q^96 - 9914 * q^97 - 23996 * q^98 - 34926 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(693))\)

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
693.4.a	\(\chi_{693}(1, \cdot)\)	693.4.a.a	1	1
		693.4.a.b	1
		693.4.a.c	1
		693.4.a.d	1
		693.4.a.e	1
		693.4.a.f	1
		693.4.a.g	2
		693.4.a.h	2
		693.4.a.i	2
		693.4.a.j	2
		693.4.a.k	2
		693.4.a.l	4
		693.4.a.m	4
		693.4.a.n	5
		693.4.a.o	5
		693.4.a.p	5
		693.4.a.q	5
		693.4.a.r	8
		693.4.a.s	8
		693.4.a.t	8
		693.4.a.u	8
693.4.c	\(\chi_{693}(307, \cdot)\)	n/a	118	1
693.4.e	\(\chi_{693}(188, \cdot)\)	693.4.e.a	80	1
693.4.g	\(\chi_{693}(197, \cdot)\)	693.4.g.a	72	1
693.4.i	\(\chi_{693}(100, \cdot)\)	n/a	200	2
693.4.j	\(\chi_{693}(232, \cdot)\)	n/a	360	2
693.4.k	\(\chi_{693}(67, \cdot)\)	n/a	480	2
693.4.l	\(\chi_{693}(529, \cdot)\)	n/a	480	2
693.4.m	\(\chi_{693}(64, \cdot)\)	n/a	360	4
693.4.n	\(\chi_{693}(320, \cdot)\)	n/a	480	2
693.4.p	\(\chi_{693}(241, \cdot)\)	n/a	568	2
693.4.r	\(\chi_{693}(32, \cdot)\)	n/a	568	2
693.4.w	\(\chi_{693}(428, \cdot)\)	n/a	432	2
693.4.x	\(\chi_{693}(296, \cdot)\)	n/a	192	2
693.4.ba	\(\chi_{693}(439, \cdot)\)	n/a	568	2
693.4.bd	\(\chi_{693}(419, \cdot)\)	n/a	480	2
693.4.be	\(\chi_{693}(89, \cdot)\)	n/a	160	2
693.4.bg	\(\chi_{693}(10, \cdot)\)	n/a	236	2
693.4.bj	\(\chi_{693}(76, \cdot)\)	n/a	568	2
693.4.bk	\(\chi_{693}(122, \cdot)\)	n/a	480	2
693.4.bn	\(\chi_{693}(263, \cdot)\)	n/a	568	2
693.4.bq	\(\chi_{693}(8, \cdot)\)	n/a	288	4
693.4.bs	\(\chi_{693}(125, \cdot)\)	n/a	384	4
693.4.bu	\(\chi_{693}(118, \cdot)\)	n/a	472	4
693.4.bw	\(\chi_{693}(25, \cdot)\)	n/a	2272	8
693.4.bx	\(\chi_{693}(4, \cdot)\)	n/a	2272	8
693.4.by	\(\chi_{693}(37, \cdot)\)	n/a	944	8
693.4.bz	\(\chi_{693}(148, \cdot)\)	n/a	1728	8
693.4.cb	\(\chi_{693}(74, \cdot)\)	n/a	2272	8
693.4.ce	\(\chi_{693}(47, \cdot)\)	n/a	2272	8
693.4.cg	\(\chi_{693}(19, \cdot)\)	n/a	944	8
693.4.ch	\(\chi_{693}(13, \cdot)\)	n/a	2272	8
693.4.cj	\(\chi_{693}(20, \cdot)\)	n/a	2272	8
693.4.cm	\(\chi_{693}(26, \cdot)\)	n/a	768	8
693.4.co	\(\chi_{693}(61, \cdot)\)	n/a	2272	8
693.4.cq	\(\chi_{693}(29, \cdot)\)	n/a	1728	8
693.4.ct	\(\chi_{693}(107, \cdot)\)	n/a	768	8
693.4.cx	\(\chi_{693}(2, \cdot)\)	n/a	2272	8
693.4.cz	\(\chi_{693}(40, \cdot)\)	n/a	2272	8
693.4.db	\(\chi_{693}(5, \cdot)\)	n/a	2272	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(693))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(693)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)