Space of modular forms of level 1323 and weight 4

• Label: 1323.4
• Level: 1323
• Weight: 4
• Dimension: 143672
• Nonzero newspaces: 32
• Sturm bound: 508032
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(508032\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1323))\).

	Total	New	Old
Modular forms	192312	145224	47088
Cusp forms	188712	143672	45040
Eisenstein series	3600	1552	2048

Trace form

143672 * q - 123 * q^2 - 186 * q^3 - 199 * q^4 - 99 * q^5 - 198 * q^6 - 252 * q^7 - 357 * q^8 - 234 * q^9 - 255 * q^10 + 3 * q^11 - 33 * q^12 + 37 * q^13 + 120 * q^14 - 360 * q^15 - 415 * q^16 - 813 * q^17 - 819 * q^18 - 809 * q^19 - 2157 * q^20 - 216 * q^21 - 1215 * q^22 - 189 * q^23 + 990 * q^24 + 215 * q^25 + 2898 * q^26 + 945 * q^27 + 144 * q^28 + 1461 * q^29 + 279 * q^30 + 1369 * q^31 + 2517 * q^32 - 819 * q^33 + 861 * q^34 - 108 * q^35 - 2412 * q^36 - 2015 * q^37 - 5685 * q^38 - 948 * q^39 - 5703 * q^40 - 5643 * q^41 - 216 * q^42 - 2075 * q^43 - 6393 * q^44 - 540 * q^45 - 1857 * q^46 + 471 * q^47 - 5667 * q^48 - 2532 * q^49 - 15294 * q^50 - 5085 * q^51 - 3731 * q^52 - 1524 * q^53 + 3114 * q^54 + 4272 * q^55 + 7914 * q^56 + 7710 * q^57 + 12525 * q^58 + 17916 * q^59 + 25326 * q^60 + 7141 * q^61 + 27234 * q^62 + 7596 * q^63 + 20423 * q^64 + 18075 * q^65 + 3105 * q^66 + 4495 * q^67 + 21960 * q^68 - 2718 * q^69 + 5292 * q^70 - 1449 * q^71 - 10296 * q^72 - 6335 * q^73 - 19785 * q^74 - 14496 * q^75 - 19679 * q^76 - 16416 * q^77 - 19890 * q^78 - 12875 * q^79 - 36582 * q^80 + 3258 * q^81 - 11202 * q^82 - 7779 * q^83 - 216 * q^84 - 6219 * q^85 - 7287 * q^86 + 2700 * q^87 + 3825 * q^88 - 5274 * q^89 - 12690 * q^90 + 108 * q^91 - 13887 * q^92 - 11982 * q^93 - 4791 * q^94 - 4653 * q^95 - 14274 * q^96 + 361 * q^97 + 3774 * q^98 - 1818 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1323))\)

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
1323.4.a	\(\chi_{1323}(1, \cdot)\)	1323.4.a.a	1	1
		1323.4.a.b	1
		1323.4.a.c	1
		1323.4.a.d	1
		1323.4.a.e	1
		1323.4.a.f	1
		1323.4.a.g	1
		1323.4.a.h	1
		1323.4.a.i	1
		1323.4.a.j	1
		1323.4.a.k	1
		1323.4.a.l	1
		1323.4.a.m	1
		1323.4.a.n	1
		1323.4.a.o	2
		1323.4.a.p	2
		1323.4.a.q	2
		1323.4.a.r	2
		1323.4.a.s	2
		1323.4.a.t	2
		1323.4.a.u	2
		1323.4.a.v	2
		1323.4.a.w	2
		1323.4.a.x	2
		1323.4.a.y	3
		1323.4.a.z	3
		1323.4.a.ba	4
		1323.4.a.bb	6
		1323.4.a.bc	6
		1323.4.a.bd	6
		1323.4.a.be	6
		1323.4.a.bf	6
		1323.4.a.bg	6
		1323.4.a.bh	7
		1323.4.a.bi	7
		1323.4.a.bj	7
		1323.4.a.bk	7
		1323.4.a.bl	8
		1323.4.a.bm	8
		1323.4.a.bn	8
		1323.4.a.bo	8
		1323.4.a.bp	12
		1323.4.a.bq	12
1323.4.c	\(\chi_{1323}(1322, \cdot)\)	n/a	160	1
1323.4.e	\(\chi_{1323}(1108, \cdot)\)	n/a	320	2
1323.4.f	\(\chi_{1323}(442, \cdot)\)	n/a	236	2
1323.4.g	\(\chi_{1323}(361, \cdot)\)	n/a	232	2
1323.4.h	\(\chi_{1323}(226, \cdot)\)	n/a	232	2
1323.4.i	\(\chi_{1323}(521, \cdot)\)	n/a	232	2
1323.4.o	\(\chi_{1323}(440, \cdot)\)	n/a	232	2
1323.4.p	\(\chi_{1323}(80, \cdot)\)	n/a	320	2
1323.4.s	\(\chi_{1323}(656, \cdot)\)	n/a	232	2
1323.4.u	\(\chi_{1323}(190, \cdot)\)	n/a	1344	6
1323.4.v	\(\chi_{1323}(67, \cdot)\)	n/a	2136	6
1323.4.w	\(\chi_{1323}(148, \cdot)\)	n/a	2184	6
1323.4.x	\(\chi_{1323}(214, \cdot)\)	n/a	2136	6
1323.4.z	\(\chi_{1323}(188, \cdot)\)	n/a	1344	6
1323.4.be	\(\chi_{1323}(68, \cdot)\)	n/a	2136	6
1323.4.bh	\(\chi_{1323}(362, \cdot)\)	n/a	2136	6
1323.4.bi	\(\chi_{1323}(146, \cdot)\)	n/a	2136	6
1323.4.bk	\(\chi_{1323}(37, \cdot)\)	n/a	1992	12
1323.4.bl	\(\chi_{1323}(100, \cdot)\)	n/a	1992	12
1323.4.bm	\(\chi_{1323}(64, \cdot)\)	n/a	1992	12
1323.4.bn	\(\chi_{1323}(109, \cdot)\)	n/a	2688	12
1323.4.bp	\(\chi_{1323}(17, \cdot)\)	n/a	1992	12
1323.4.bs	\(\chi_{1323}(26, \cdot)\)	n/a	2688	12
1323.4.bt	\(\chi_{1323}(62, \cdot)\)	n/a	1992	12
1323.4.bz	\(\chi_{1323}(143, \cdot)\)	n/a	1992	12
1323.4.ca	\(\chi_{1323}(25, \cdot)\)	n/a	18072	36
1323.4.cb	\(\chi_{1323}(22, \cdot)\)	n/a	18072	36
1323.4.cc	\(\chi_{1323}(4, \cdot)\)	n/a	18072	36
1323.4.ce	\(\chi_{1323}(20, \cdot)\)	n/a	18072	36
1323.4.cf	\(\chi_{1323}(47, \cdot)\)	n/a	18072	36
1323.4.ci	\(\chi_{1323}(5, \cdot)\)	n/a	18072	36

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1323))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1323)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 2}\)