Space of modular forms of level 483 and weight 4

• Label: 483.4
• Level: 483
• Weight: 4
• Dimension: 17936
• Nonzero newspaces: 16
• Sturm bound: 67584
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(67584\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(483))\).

	Total	New	Old
Modular forms	25872	18352	7520
Cusp forms	24816	17936	6880
Eisenstein series	1056	416	640

Trace form

17936 * q - 50 * q^3 - 76 * q^4 + 48 * q^5 + 28 * q^6 - 2 * q^7 - 108 * q^8 - 122 * q^9 - 184 * q^10 + 148 * q^12 + 80 * q^13 + 624 * q^14 - 462 * q^15 - 1596 * q^16 - 328 * q^17 - 408 * q^18 - 764 * q^19 + 728 * q^20 - 565 * q^21 + 808 * q^22 + 2104 * q^23 + 2264 * q^24 + 2172 * q^25 + 1468 * q^26 + 304 * q^27 + 1406 * q^28 + 416 * q^29 + 24 * q^30 - 788 * q^31 - 3548 * q^32 - 378 * q^33 - 7192 * q^34 - 3028 * q^35 - 2606 * q^36 - 7684 * q^37 - 5840 * q^38 - 2204 * q^39 + 2360 * q^40 + 1816 * q^41 - 1069 * q^42 + 4340 * q^43 + 8876 * q^44 - 4368 * q^45 + 15044 * q^46 + 5984 * q^47 + 8756 * q^48 + 8938 * q^49 + 14216 * q^50 + 7414 * q^51 + 10592 * q^52 + 3232 * q^53 + 13332 * q^54 - 5968 * q^55 - 8530 * q^56 - 3242 * q^57 - 31564 * q^58 - 11384 * q^59 - 12544 * q^60 - 6364 * q^61 - 3624 * q^62 - 6711 * q^63 - 8776 * q^64 - 1008 * q^65 - 13314 * q^66 - 1924 * q^67 + 3072 * q^68 - 5868 * q^69 + 6788 * q^70 + 984 * q^71 - 6728 * q^72 + 8564 * q^73 - 4000 * q^74 - 15368 * q^75 - 21780 * q^76 - 10112 * q^77 - 18234 * q^78 - 10508 * q^79 - 22428 * q^80 - 5290 * q^81 - 14800 * q^82 - 5056 * q^83 + 775 * q^84 + 12004 * q^85 + 16508 * q^86 + 15388 * q^87 + 28528 * q^88 + 25944 * q^89 + 39494 * q^90 + 14276 * q^91 + 40740 * q^92 + 24674 * q^93 + 32212 * q^94 + 13416 * q^95 + 16378 * q^96 - 9928 * q^97 - 862 * q^98 + 12478 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(483))\)

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
483.4.a	\(\chi_{483}(1, \cdot)\)	483.4.a.a	3	1
		483.4.a.b	4
		483.4.a.c	7
		483.4.a.d	7
		483.4.a.e	7
		483.4.a.f	9
		483.4.a.g	9
		483.4.a.h	9
		483.4.a.i	9
483.4.d	\(\chi_{483}(461, \cdot)\)	n/a	176	1
483.4.e	\(\chi_{483}(344, \cdot)\)	n/a	144	1
483.4.h	\(\chi_{483}(160, \cdot)\)	483.4.h.a	96	1
483.4.i	\(\chi_{483}(277, \cdot)\)	n/a	176	2
483.4.j	\(\chi_{483}(229, \cdot)\)	n/a	192	2
483.4.m	\(\chi_{483}(137, \cdot)\)	n/a	376	2
483.4.n	\(\chi_{483}(47, \cdot)\)	n/a	352	2
483.4.q	\(\chi_{483}(64, \cdot)\)	n/a	720	10
483.4.r	\(\chi_{483}(34, \cdot)\)	n/a	960	10
483.4.u	\(\chi_{483}(113, \cdot)\)	n/a	1440	10
483.4.v	\(\chi_{483}(41, \cdot)\)	n/a	1880	10
483.4.y	\(\chi_{483}(4, \cdot)\)	n/a	1920	20
483.4.bb	\(\chi_{483}(26, \cdot)\)	n/a	3760	20
483.4.bc	\(\chi_{483}(11, \cdot)\)	n/a	3760	20
483.4.bf	\(\chi_{483}(10, \cdot)\)	n/a	1920	20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(483))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(483)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 1}\)