Space of modular forms of level 2366 and weight 2

• Label: 2366.2
• Level: 2366
• Weight: 2
• Dimension: 53774
• Nonzero newspaces: 30
• Sturm bound: 681408
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(681408\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2366))\).

	Total	New	Old
Modular forms	173088	53774	119314
Cusp forms	167617	53774	113843
Eisenstein series	5471	0	5471

Trace form

53774 * q - 2 * q^2 - 6 * q^3 - 6 * q^5 - 2 * q^6 + 8 * q^7 + 10 * q^8 + 52 * q^9 + 54 * q^10 + 36 * q^11 + 10 * q^12 + 48 * q^13 + 22 * q^14 + 72 * q^15 + 16 * q^16 + 48 * q^17 + 46 * q^18 + 94 * q^19 + 6 * q^20 + 50 * q^21 - 12 * q^22 + 24 * q^23 - 2 * q^24 + 24 * q^25 + 108 * q^27 + 8 * q^28 + 120 * q^29 + 72 * q^30 + 124 * q^31 - 2 * q^32 + 192 * q^33 + 72 * q^34 + 138 * q^35 + 84 * q^36 + 88 * q^37 + 122 * q^38 + 104 * q^39 - 6 * q^40 + 168 * q^41 + 70 * q^42 + 140 * q^43 + 84 * q^44 + 222 * q^45 + 72 * q^46 + 132 * q^47 - 6 * q^48 + 64 * q^49 + 82 * q^50 + 204 * q^51 + 14 * q^52 + 96 * q^53 + 100 * q^54 + 168 * q^55 + 22 * q^56 + 172 * q^57 + 84 * q^58 + 126 * q^59 + 72 * q^60 + 102 * q^61 + 116 * q^62 + 236 * q^63 + 12 * q^64 + 174 * q^65 + 144 * q^66 + 232 * q^67 + 384 * q^69 + 66 * q^70 + 216 * q^71 + 82 * q^72 + 232 * q^73 - 28 * q^74 + 142 * q^75 - 98 * q^76 - 204 * q^77 - 24 * q^78 - 264 * q^79 + 6 * q^80 - 260 * q^81 - 420 * q^82 - 138 * q^83 - 286 * q^84 - 480 * q^85 - 244 * q^86 - 492 * q^87 - 12 * q^88 - 288 * q^89 - 558 * q^90 - 236 * q^91 - 216 * q^92 - 296 * q^93 - 516 * q^94 - 408 * q^95 - 2 * q^96 - 572 * q^97 - 194 * q^98 - 588 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2366))\)

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
2366.2.a	\(\chi_{2366}(1, \cdot)\)	2366.2.a.a	1	1
		2366.2.a.b	1
		2366.2.a.c	1
		2366.2.a.d	1
		2366.2.a.e	1
		2366.2.a.f	1
		2366.2.a.g	1
		2366.2.a.h	1
		2366.2.a.i	1
		2366.2.a.j	1
		2366.2.a.k	1
		2366.2.a.l	1
		2366.2.a.m	1
		2366.2.a.n	1
		2366.2.a.o	1
		2366.2.a.p	1
		2366.2.a.q	2
		2366.2.a.r	2
		2366.2.a.s	2
		2366.2.a.t	2
		2366.2.a.u	3
		2366.2.a.v	3
		2366.2.a.w	3
		2366.2.a.x	3
		2366.2.a.y	3
		2366.2.a.z	3
		2366.2.a.ba	3
		2366.2.a.bb	3
		2366.2.a.bc	3
		2366.2.a.bd	3
		2366.2.a.be	6
		2366.2.a.bf	6
		2366.2.a.bg	6
		2366.2.a.bh	6
2366.2.d	\(\chi_{2366}(337, \cdot)\)	2366.2.d.a	2	1
		2366.2.d.b	2
		2366.2.d.c	2
		2366.2.d.d	2
		2366.2.d.e	2
		2366.2.d.f	2
		2366.2.d.g	2
		2366.2.d.h	2
		2366.2.d.i	2
		2366.2.d.j	2
		2366.2.d.k	4
		2366.2.d.l	4
		2366.2.d.m	6
		2366.2.d.n	6
		2366.2.d.o	6
		2366.2.d.p	6
		2366.2.d.q	12
		2366.2.d.r	12
2366.2.e	\(\chi_{2366}(529, \cdot)\)	n/a	204	2
2366.2.f	\(\chi_{2366}(1353, \cdot)\)	n/a	208	2
2366.2.g	\(\chi_{2366}(1205, \cdot)\)	n/a	156	2
2366.2.h	\(\chi_{2366}(191, \cdot)\)	n/a	204	2
2366.2.i	\(\chi_{2366}(2127, \cdot)\)	n/a	200	2
2366.2.m	\(\chi_{2366}(1037, \cdot)\)	n/a	152	2
2366.2.n	\(\chi_{2366}(1689, \cdot)\)	n/a	208	2
2366.2.o	\(\chi_{2366}(23, \cdot)\)	n/a	204	2
2366.2.v	\(\chi_{2366}(361, \cdot)\)	n/a	204	2
2366.2.w	\(\chi_{2366}(19, \cdot)\)	n/a	408	4
2366.2.ba	\(\chi_{2366}(587, \cdot)\)	n/a	416	4
2366.2.bb	\(\chi_{2366}(437, \cdot)\)	n/a	416	4
2366.2.bc	\(\chi_{2366}(89, \cdot)\)	n/a	408	4
2366.2.be	\(\chi_{2366}(183, \cdot)\)	n/a	1080	12
2366.2.bf	\(\chi_{2366}(155, \cdot)\)	n/a	1104	12
2366.2.bi	\(\chi_{2366}(9, \cdot)\)	n/a	2928	24
2366.2.bj	\(\chi_{2366}(29, \cdot)\)	n/a	2160	24
2366.2.bk	\(\chi_{2366}(53, \cdot)\)	n/a	2880	24
2366.2.bl	\(\chi_{2366}(107, \cdot)\)	n/a	2928	24
2366.2.bn	\(\chi_{2366}(83, \cdot)\)	n/a	2976	24
2366.2.bo	\(\chi_{2366}(121, \cdot)\)	n/a	2928	24
2366.2.bv	\(\chi_{2366}(95, \cdot)\)	n/a	2928	24
2366.2.bw	\(\chi_{2366}(25, \cdot)\)	n/a	2880	24
2366.2.bx	\(\chi_{2366}(43, \cdot)\)	n/a	2208	24
2366.2.cb	\(\chi_{2366}(45, \cdot)\)	n/a	5856	48
2366.2.cc	\(\chi_{2366}(5, \cdot)\)	n/a	5760	48
2366.2.cd	\(\chi_{2366}(41, \cdot)\)	n/a	5760	48
2366.2.ch	\(\chi_{2366}(33, \cdot)\)	n/a	5856	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2366))\) into lower level spaces

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