Space of modular forms of level 2370 and weight 2

• Label: 2370.2
• Level: 2370
• Weight: 2
• Dimension: 34305
• Nonzero newspaces: 24
• Sturm bound: 599040
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 2370 = 2 \cdot 3 \cdot 5 \cdot 79 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(599040\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2370))\).

	Total	New	Old
Modular forms	152256	34305	117951
Cusp forms	147265	34305	112960
Eisenstein series	4991	0	4991

Trace form

34305 * q + q^2 + 5 * q^3 + q^4 + 9 * q^5 + 5 * q^6 + 8 * q^7 + q^8 + q^9 - 7 * q^10 - 20 * q^11 - 11 * q^12 - 18 * q^13 - 24 * q^14 - 19 * q^15 + q^16 - 30 * q^17 - 15 * q^18 - 12 * q^19 - 7 * q^20 - 8 * q^21 - 4 * q^22 - 24 * q^23 + 5 * q^24 + 17 * q^25 + 14 * q^26 + 5 * q^27 + 8 * q^28 - 18 * q^29 + 29 * q^30 + q^32 - 4 * q^33 - 14 * q^34 - 24 * q^35 + q^36 - 90 * q^37 - 28 * q^38 - 42 * q^39 - 23 * q^40 - 38 * q^41 - 24 * q^42 - 84 * q^43 - 4 * q^44 + 9 * q^45 - 72 * q^46 - 48 * q^47 - 11 * q^48 - 87 * q^49 - 15 * q^50 - 6 * q^51 - 18 * q^52 - 42 * q^53 + 5 * q^54 - 20 * q^55 - 8 * q^56 + 20 * q^57 - 2 * q^58 - 20 * q^59 + 13 * q^60 - 2 * q^61 - 16 * q^62 + 60 * q^63 + q^64 + 326 * q^65 + 276 * q^66 + 700 * q^67 + 282 * q^68 + 616 * q^69 + 632 * q^70 + 504 * q^71 + 17 * q^72 + 586 * q^73 + 582 * q^74 + 269 * q^75 + 684 * q^76 + 840 * q^77 + 302 * q^78 + 1785 * q^79 + 9 * q^80 - 63 * q^81 + 602 * q^82 + 828 * q^83 + 356 * q^84 + 594 * q^85 + 556 * q^86 + 254 * q^87 - 4 * q^88 + 458 * q^89 + 55 * q^90 + 1104 * q^91 + 288 * q^92 + 300 * q^93 + 608 * q^94 + 284 * q^95 - 11 * q^96 + 290 * q^97 - 39 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2370))\)

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
2370.2.a	\(\chi_{2370}(1, \cdot)\)	2370.2.a.a	1	1
		2370.2.a.b	1
		2370.2.a.c	1
		2370.2.a.d	1
		2370.2.a.e	1
		2370.2.a.f	1
		2370.2.a.g	1
		2370.2.a.h	1
		2370.2.a.i	1
		2370.2.a.j	1
		2370.2.a.k	1
		2370.2.a.l	1
		2370.2.a.m	1
		2370.2.a.n	1
		2370.2.a.o	1
		2370.2.a.p	2
		2370.2.a.q	2
		2370.2.a.r	2
		2370.2.a.s	2
		2370.2.a.t	3
		2370.2.a.u	3
		2370.2.a.v	3
		2370.2.a.w	3
		2370.2.a.x	3
		2370.2.a.y	3
		2370.2.a.z	4
		2370.2.a.ba	4
		2370.2.a.bb	4
2370.2.c	\(\chi_{2370}(1421, \cdot)\)	n/a	104	1
2370.2.d	\(\chi_{2370}(949, \cdot)\)	2370.2.d.a	2	1
		2370.2.d.b	2
		2370.2.d.c	2
		2370.2.d.d	8
		2370.2.d.e	14
		2370.2.d.f	24
		2370.2.d.g	24
2370.2.f	\(\chi_{2370}(2369, \cdot)\)	n/a	160	1
2370.2.i	\(\chi_{2370}(181, \cdot)\)	n/a	104	2
2370.2.k	\(\chi_{2370}(317, \cdot)\)	n/a	312	2
2370.2.m	\(\chi_{2370}(157, \cdot)\)	n/a	160	2
2370.2.p	\(\chi_{2370}(419, \cdot)\)	n/a	320	2
2370.2.r	\(\chi_{2370}(529, \cdot)\)	n/a	160	2
2370.2.s	\(\chi_{2370}(1241, \cdot)\)	n/a	216	2
2370.2.u	\(\chi_{2370}(103, \cdot)\)	n/a	320	4
2370.2.w	\(\chi_{2370}(23, \cdot)\)	n/a	640	4
2370.2.y	\(\chi_{2370}(301, \cdot)\)	n/a	672	12
2370.2.bb	\(\chi_{2370}(659, \cdot)\)	n/a	1920	12
2370.2.bd	\(\chi_{2370}(259, \cdot)\)	n/a	960	12
2370.2.be	\(\chi_{2370}(41, \cdot)\)	n/a	1248	12
2370.2.bg	\(\chi_{2370}(31, \cdot)\)	n/a	1248	24
2370.2.bh	\(\chi_{2370}(343, \cdot)\)	n/a	1920	24
2370.2.bj	\(\chi_{2370}(143, \cdot)\)	n/a	3840	24
2370.2.bm	\(\chi_{2370}(161, \cdot)\)	n/a	2592	24
2370.2.bn	\(\chi_{2370}(19, \cdot)\)	n/a	1920	24
2370.2.bp	\(\chi_{2370}(29, \cdot)\)	n/a	3840	24
2370.2.bt	\(\chi_{2370}(83, \cdot)\)	n/a	7680	48
2370.2.bv	\(\chi_{2370}(7, \cdot)\)	n/a	3840	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2370))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2370)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(158))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(237))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(395))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(474))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(790))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1185))\)\(^{\oplus 2}\)