Space of modular forms of level 2370 and weight 4

• Label: 2370.4
• Level: 2370
• Weight: 4
• Dimension: 102928
• Nonzero newspaces: 24
• Sturm bound: 1198080
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 2370 = 2 \cdot 3 \cdot 5 \cdot 79 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(1198080\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2370))\).

	Total	New	Old
Modular forms	451776	102928	348848
Cusp forms	446784	102928	343856
Eisenstein series	4992	0	4992

Trace form

102928 * q - 28 * q^3 - 8 * q^5 + 8 * q^6 - 80 * q^7 + 80 * q^10 - 64 * q^11 + 16 * q^12 + 304 * q^13 + 128 * q^14 + 476 * q^15 + 256 * q^16 + 144 * q^17 + 32 * q^18 - 32 * q^19 + 32 * q^20 - 1120 * q^21 - 672 * q^22 - 144 * q^23 - 96 * q^24 - 640 * q^25 - 576 * q^26 + 1268 * q^27 - 320 * q^28 + 432 * q^29 - 168 * q^30 + 96 * q^31 - 928 * q^33 + 448 * q^34 - 448 * q^35 - 1024 * q^36 - 1136 * q^37 - 864 * q^38 - 456 * q^39 + 192 * q^40 + 752 * q^41 + 2176 * q^42 + 5296 * q^43 + 1984 * q^44 + 2728 * q^45 + 2816 * q^46 + 288 * q^47 + 64 * q^48 - 2064 * q^49 + 352 * q^50 - 344 * q^51 - 704 * q^52 - 288 * q^53 - 216 * q^54 - 3584 * q^55 + 640 * q^56 - 2320 * q^57 - 5376 * q^58 - 3280 * q^59 - 2320 * q^60 - 1120 * q^61 - 2016 * q^62 + 5384 * q^63 + 30432 * q^65 + 23984 * q^66 + 40000 * q^67 + 10560 * q^68 + 8256 * q^69 + 2016 * q^70 - 10272 * q^71 - 128 * q^72 - 30848 * q^73 - 36352 * q^74 - 18140 * q^75 - 51008 * q^76 - 67680 * q^77 - 16608 * q^78 - 143944 * q^79 - 128 * q^80 + 7984 * q^81 - 43872 * q^82 - 51984 * q^83 - 18048 * q^84 - 21248 * q^85 - 16640 * q^86 - 10408 * q^87 - 2688 * q^88 + 17152 * q^89 - 6556 * q^90 + 91808 * q^91 + 31872 * q^92 + 46640 * q^93 + 96224 * q^94 + 62880 * q^95 + 640 * q^96 + 127696 * q^97 + 4032 * q^98 + 4464 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2370))\)

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
2370.4.a	\(\chi_{2370}(1, \cdot)\)	2370.4.a.a	1	1
		2370.4.a.b	7
		2370.4.a.c	7
		2370.4.a.d	8
		2370.4.a.e	8
		2370.4.a.f	9
		2370.4.a.g	9
		2370.4.a.h	9
		2370.4.a.i	10
		2370.4.a.j	10
		2370.4.a.k	10
		2370.4.a.l	10
		2370.4.a.m	11
		2370.4.a.n	11
		2370.4.a.o	11
		2370.4.a.p	12
		2370.4.a.q	13
2370.4.c	\(\chi_{2370}(1421, \cdot)\)	n/a	320	1
2370.4.d	\(\chi_{2370}(949, \cdot)\)	n/a	236	1
2370.4.f	\(\chi_{2370}(2369, \cdot)\)	n/a	480	1
2370.4.i	\(\chi_{2370}(181, \cdot)\)	n/a	320	2
2370.4.k	\(\chi_{2370}(317, \cdot)\)	n/a	936	2
2370.4.m	\(\chi_{2370}(157, \cdot)\)	n/a	480	2
2370.4.p	\(\chi_{2370}(419, \cdot)\)	n/a	960	2
2370.4.r	\(\chi_{2370}(529, \cdot)\)	n/a	480	2
2370.4.s	\(\chi_{2370}(1241, \cdot)\)	n/a	640	2
2370.4.u	\(\chi_{2370}(103, \cdot)\)	n/a	960	4
2370.4.w	\(\chi_{2370}(23, \cdot)\)	n/a	1920	4
2370.4.y	\(\chi_{2370}(301, \cdot)\)	n/a	1920	12
2370.4.bb	\(\chi_{2370}(659, \cdot)\)	n/a	5760	12
2370.4.bd	\(\chi_{2370}(259, \cdot)\)	n/a	2880	12
2370.4.be	\(\chi_{2370}(41, \cdot)\)	n/a	3840	12
2370.4.bg	\(\chi_{2370}(31, \cdot)\)	n/a	3840	24
2370.4.bh	\(\chi_{2370}(343, \cdot)\)	n/a	5760	24
2370.4.bj	\(\chi_{2370}(143, \cdot)\)	n/a	11520	24
2370.4.bm	\(\chi_{2370}(161, \cdot)\)	n/a	7680	24
2370.4.bn	\(\chi_{2370}(19, \cdot)\)	n/a	5760	24
2370.4.bp	\(\chi_{2370}(29, \cdot)\)	n/a	11520	24
2370.4.bt	\(\chi_{2370}(83, \cdot)\)	n/a	23040	48
2370.4.bv	\(\chi_{2370}(7, \cdot)\)	n/a	11520	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2370))\) into lower level spaces

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