Space of modular forms of level 1323 and weight 2

• Label: 1323.2
• Level: 1323
• Weight: 2
• Dimension: 47373
• Nonzero newspaces: 32
• Sturm bound: 254016
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(254016\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1323))\).

	Total	New	Old
Modular forms	65304	48925	16379
Cusp forms	61705	47373	14332
Eisenstein series	3599	1552	2047

Trace form

47373 * q - 126 * q^2 - 186 * q^3 - 218 * q^4 - 123 * q^5 - 180 * q^6 - 252 * q^7 - 210 * q^8 - 180 * q^9 - 213 * q^10 - 117 * q^11 - 168 * q^12 - 207 * q^13 - 132 * q^14 - 315 * q^15 - 166 * q^16 - 75 * q^17 - 171 * q^18 - 192 * q^19 - 39 * q^20 - 216 * q^21 - 327 * q^22 - 96 * q^23 - 198 * q^24 - 184 * q^25 - 78 * q^26 - 189 * q^27 - 556 * q^28 - 198 * q^29 - 189 * q^30 - 183 * q^31 - 12 * q^32 - 180 * q^33 - 129 * q^34 - 108 * q^35 - 306 * q^36 - 154 * q^37 + 42 * q^38 - 147 * q^39 - 117 * q^40 + 3 * q^41 - 216 * q^42 - 319 * q^43 + 39 * q^44 - 189 * q^45 - 93 * q^46 - 63 * q^47 - 411 * q^48 - 250 * q^49 - 537 * q^50 - 306 * q^51 - 315 * q^52 - 390 * q^53 - 450 * q^54 - 660 * q^55 - 402 * q^56 - 471 * q^57 - 453 * q^58 - 432 * q^59 - 612 * q^60 - 315 * q^61 - 672 * q^62 - 342 * q^63 - 758 * q^64 - 477 * q^65 - 477 * q^66 - 320 * q^67 - 747 * q^68 - 351 * q^69 - 336 * q^70 - 333 * q^71 - 522 * q^72 - 315 * q^73 - 279 * q^74 - 321 * q^75 - 276 * q^76 - 162 * q^77 - 450 * q^78 - 167 * q^79 - 282 * q^80 - 144 * q^81 - 396 * q^82 + 75 * q^83 - 216 * q^84 - 261 * q^85 + 195 * q^86 - 171 * q^87 - 120 * q^88 + 117 * q^89 - 162 * q^90 - 172 * q^91 + 57 * q^92 - 219 * q^93 + 15 * q^94 + 87 * q^95 - 180 * q^96 - 66 * q^97 - 6 * q^98 - 603 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1323))\)

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
1323.2.a	\(\chi_{1323}(1, \cdot)\)	1323.2.a.a	1	1
		1323.2.a.b	1
		1323.2.a.c	1
		1323.2.a.d	1
		1323.2.a.e	1
		1323.2.a.f	1
		1323.2.a.g	1
		1323.2.a.h	1
		1323.2.a.i	1
		1323.2.a.j	1
		1323.2.a.k	1
		1323.2.a.l	1
		1323.2.a.m	1
		1323.2.a.n	1
		1323.2.a.o	1
		1323.2.a.p	1
		1323.2.a.q	1
		1323.2.a.r	1
		1323.2.a.s	1
		1323.2.a.t	2
		1323.2.a.u	2
		1323.2.a.v	2
		1323.2.a.w	2
		1323.2.a.x	3
		1323.2.a.y	3
		1323.2.a.z	3
		1323.2.a.ba	3
		1323.2.a.bb	4
		1323.2.a.bc	4
		1323.2.a.bd	4
		1323.2.a.be	4
1323.2.c	\(\chi_{1323}(1322, \cdot)\)	1323.2.c.a	2	1
		1323.2.c.b	4
		1323.2.c.c	4
		1323.2.c.d	12
		1323.2.c.e	16
		1323.2.c.f	16
1323.2.e	\(\chi_{1323}(1108, \cdot)\)	n/a	106	2
1323.2.f	\(\chi_{1323}(442, \cdot)\)	1323.2.f.a	2	2
		1323.2.f.b	2
		1323.2.f.c	6
		1323.2.f.d	6
		1323.2.f.e	10
		1323.2.f.f	10
		1323.2.f.g	12
		1323.2.f.h	24
1323.2.g	\(\chi_{1323}(361, \cdot)\)	1323.2.g.a	2	2
		1323.2.g.b	6
		1323.2.g.c	6
		1323.2.g.d	6
		1323.2.g.e	6
		1323.2.g.f	10
		1323.2.g.g	12
		1323.2.g.h	24
1323.2.h	\(\chi_{1323}(226, \cdot)\)	1323.2.h.a	2	2
		1323.2.h.b	6
		1323.2.h.c	6
		1323.2.h.d	6
		1323.2.h.e	6
		1323.2.h.f	10
		1323.2.h.g	12
		1323.2.h.h	24
1323.2.i	\(\chi_{1323}(521, \cdot)\)	1323.2.i.a	2	2
		1323.2.i.b	10
		1323.2.i.c	12
		1323.2.i.d	48
1323.2.o	\(\chi_{1323}(440, \cdot)\)	1323.2.o.a	2	2
		1323.2.o.b	2
		1323.2.o.c	10
		1323.2.o.d	10
		1323.2.o.e	48
1323.2.p	\(\chi_{1323}(80, \cdot)\)	n/a	106	2
1323.2.s	\(\chi_{1323}(656, \cdot)\)	1323.2.s.a	2	2
		1323.2.s.b	10
		1323.2.s.c	12
		1323.2.s.d	48
1323.2.u	\(\chi_{1323}(190, \cdot)\)	n/a	444	6
1323.2.v	\(\chi_{1323}(67, \cdot)\)	n/a	696	6
1323.2.w	\(\chi_{1323}(148, \cdot)\)	n/a	708	6
1323.2.x	\(\chi_{1323}(214, \cdot)\)	n/a	696	6
1323.2.z	\(\chi_{1323}(188, \cdot)\)	n/a	444	6
1323.2.be	\(\chi_{1323}(68, \cdot)\)	n/a	696	6
1323.2.bh	\(\chi_{1323}(362, \cdot)\)	n/a	696	6
1323.2.bi	\(\chi_{1323}(146, \cdot)\)	n/a	696	6
1323.2.bk	\(\chi_{1323}(37, \cdot)\)	n/a	648	12
1323.2.bl	\(\chi_{1323}(100, \cdot)\)	n/a	648	12
1323.2.bm	\(\chi_{1323}(64, \cdot)\)	n/a	648	12
1323.2.bn	\(\chi_{1323}(109, \cdot)\)	n/a	900	12
1323.2.bp	\(\chi_{1323}(17, \cdot)\)	n/a	648	12
1323.2.bs	\(\chi_{1323}(26, \cdot)\)	n/a	900	12
1323.2.bt	\(\chi_{1323}(62, \cdot)\)	n/a	648	12
1323.2.bz	\(\chi_{1323}(143, \cdot)\)	n/a	648	12
1323.2.ca	\(\chi_{1323}(25, \cdot)\)	n/a	5976	36
1323.2.cb	\(\chi_{1323}(22, \cdot)\)	n/a	5976	36
1323.2.cc	\(\chi_{1323}(4, \cdot)\)	n/a	5976	36
1323.2.ce	\(\chi_{1323}(20, \cdot)\)	n/a	5976	36
1323.2.cf	\(\chi_{1323}(47, \cdot)\)	n/a	5976	36
1323.2.ci	\(\chi_{1323}(5, \cdot)\)	n/a	5976	36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1323))\) into lower level spaces

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