Space of modular forms of level 2366 and weight 4

• Label: 2366.4
• Level: 2366
• Weight: 4
• Dimension: 161328
• Nonzero newspaces: 30
• Sturm bound: 1362816
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(1362816\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2366))\).

	Total	New	Old
Modular forms	513792	161328	352464
Cusp forms	508320	161328	346992
Eisenstein series	5472	0	5472

Trace form

161328 * q + 12 * q^3 - 24 * q^5 - 36 * q^6 + 96 * q^7 + 96 * q^8 + 42 * q^9 - 324 * q^10 - 438 * q^11 - 144 * q^12 - 576 * q^13 - 108 * q^14 - 588 * q^15 + 798 * q^17 + 912 * q^18 + 2676 * q^19 + 408 * q^20 + 168 * q^21 - 216 * q^22 - 1206 * q^23 - 48 * q^24 - 1290 * q^25 - 2736 * q^27 + 696 * q^28 + 4788 * q^29 + 3432 * q^30 + 2466 * q^31 + 1254 * q^33 - 2136 * q^34 - 1980 * q^35 - 3240 * q^36 - 2706 * q^37 - 5364 * q^38 - 2808 * q^39 + 144 * q^40 - 6228 * q^41 - 1548 * q^42 - 1188 * q^43 - 600 * q^44 + 342 * q^45 + 1560 * q^46 + 3390 * q^47 - 96 * q^48 + 3582 * q^49 + 10800 * q^50 + 18894 * q^51 + 1704 * q^52 + 5478 * q^53 + 6480 * q^54 + 1332 * q^55 + 240 * q^56 - 1944 * q^57 - 2880 * q^58 - 4920 * q^59 - 4728 * q^60 - 1812 * q^61 - 8232 * q^62 - 1488 * q^63 - 384 * q^64 + 330 * q^65 - 12288 * q^66 - 7002 * q^67 - 1224 * q^68 - 16836 * q^69 - 3204 * q^70 - 9624 * q^71 - 1440 * q^72 - 17298 * q^73 - 13152 * q^74 - 39366 * q^75 - 10632 * q^76 - 31662 * q^77 + 2160 * q^78 - 8262 * q^79 + 1728 * q^80 + 7572 * q^81 + 8832 * q^82 - 1494 * q^83 + 12528 * q^84 + 33636 * q^85 + 14280 * q^86 + 49728 * q^87 + 1344 * q^88 + 49158 * q^89 + 45588 * q^90 + 25920 * q^91 + 16464 * q^92 + 59382 * q^93 + 36624 * q^94 + 46806 * q^95 - 192 * q^96 + 37392 * q^97 + 16368 * q^98 + 33996 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2366))\)

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
2366.4.a	\(\chi_{2366}(1, \cdot)\)	2366.4.a.a	1	1
		2366.4.a.b	1
		2366.4.a.c	1
		2366.4.a.d	1
		2366.4.a.e	1
		2366.4.a.f	1
		2366.4.a.g	1
		2366.4.a.h	1
		2366.4.a.i	2
		2366.4.a.j	2
		2366.4.a.k	2
		2366.4.a.l	2
		2366.4.a.m	3
		2366.4.a.n	3
		2366.4.a.o	3
		2366.4.a.p	3
		2366.4.a.q	4
		2366.4.a.r	4
		2366.4.a.s	5
		2366.4.a.t	5
		2366.4.a.u	6
		2366.4.a.v	6
		2366.4.a.w	6
		2366.4.a.x	6
		2366.4.a.y	7
		2366.4.a.z	7
		2366.4.a.ba	8
		2366.4.a.bb	8
		2366.4.a.bc	12
		2366.4.a.bd	12
		2366.4.a.be	12
		2366.4.a.bf	12
		2366.4.a.bg	12
		2366.4.a.bh	12
		2366.4.a.bi	15
		2366.4.a.bj	15
		2366.4.a.bk	15
		2366.4.a.bl	15
2366.4.d	\(\chi_{2366}(337, \cdot)\)	n/a	232	1
2366.4.e	\(\chi_{2366}(529, \cdot)\)	n/a	616	2
2366.4.f	\(\chi_{2366}(1353, \cdot)\)	n/a	620	2
2366.4.g	\(\chi_{2366}(1205, \cdot)\)	n/a	460	2
2366.4.h	\(\chi_{2366}(191, \cdot)\)	n/a	616	2
2366.4.i	\(\chi_{2366}(2127, \cdot)\)	n/a	616	2
2366.4.m	\(\chi_{2366}(1037, \cdot)\)	n/a	464	2
2366.4.n	\(\chi_{2366}(1689, \cdot)\)	n/a	616	2
2366.4.o	\(\chi_{2366}(23, \cdot)\)	n/a	616	2
2366.4.v	\(\chi_{2366}(361, \cdot)\)	n/a	616	2
2366.4.w	\(\chi_{2366}(19, \cdot)\)	n/a	1232	4
2366.4.ba	\(\chi_{2366}(587, \cdot)\)	n/a	1232	4
2366.4.bb	\(\chi_{2366}(437, \cdot)\)	n/a	1232	4
2366.4.bc	\(\chi_{2366}(89, \cdot)\)	n/a	1232	4
2366.4.be	\(\chi_{2366}(183, \cdot)\)	n/a	3288	12
2366.4.bf	\(\chi_{2366}(155, \cdot)\)	n/a	3264	12
2366.4.bi	\(\chi_{2366}(9, \cdot)\)	n/a	8736	24
2366.4.bj	\(\chi_{2366}(29, \cdot)\)	n/a	6576	24
2366.4.bk	\(\chi_{2366}(53, \cdot)\)	n/a	8736	24
2366.4.bl	\(\chi_{2366}(107, \cdot)\)	n/a	8736	24
2366.4.bn	\(\chi_{2366}(83, \cdot)\)	n/a	8736	24
2366.4.bo	\(\chi_{2366}(121, \cdot)\)	n/a	8736	24
2366.4.bv	\(\chi_{2366}(95, \cdot)\)	n/a	8736	24
2366.4.bw	\(\chi_{2366}(25, \cdot)\)	n/a	8736	24
2366.4.bx	\(\chi_{2366}(43, \cdot)\)	n/a	6528	24
2366.4.cb	\(\chi_{2366}(45, \cdot)\)	n/a	17472	48
2366.4.cc	\(\chi_{2366}(5, \cdot)\)	n/a	17472	48
2366.4.cd	\(\chi_{2366}(41, \cdot)\)	n/a	17472	48
2366.4.ch	\(\chi_{2366}(33, \cdot)\)	n/a	17472	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2366))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2366)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 2}\)