Space of modular forms of level 539 and weight 4

• Label: 539.4
• Level: 539
• Weight: 4
• Dimension: 32854
• Nonzero newspaces: 16
• Sturm bound: 94080
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(94080\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(539))\).

	Total	New	Old
Modular forms	35880	33726	2154
Cusp forms	34680	32854	1826
Eisenstein series	1200	872	328

Trace form

32854 * q - 125 * q^2 - 149 * q^3 - 125 * q^4 - 77 * q^5 - 43 * q^6 - 96 * q^7 - 289 * q^8 - 213 * q^9 - 138 * q^10 - 90 * q^11 + 60 * q^12 - 93 * q^13 - 96 * q^14 - 243 * q^15 - 265 * q^16 + 37 * q^17 - 202 * q^18 - 524 * q^19 - 350 * q^20 - 600 * q^21 + 370 * q^22 + 460 * q^23 + 249 * q^24 + 655 * q^25 - 288 * q^26 - 98 * q^27 + 240 * q^28 - 223 * q^29 - 752 * q^30 - 1043 * q^31 - 1172 * q^32 - 237 * q^33 - 1160 * q^34 - 264 * q^35 + 3676 * q^36 + 2871 * q^37 + 5528 * q^38 + 4941 * q^39 + 7612 * q^40 + 4597 * q^41 - 390 * q^42 - 2894 * q^43 - 4705 * q^44 - 9026 * q^45 - 8722 * q^46 - 4191 * q^47 - 14654 * q^48 - 7908 * q^49 - 9743 * q^50 - 7418 * q^51 - 13354 * q^52 - 6305 * q^53 - 7974 * q^54 - 2760 * q^55 + 144 * q^56 + 4038 * q^57 + 8124 * q^58 + 10070 * q^59 + 37400 * q^60 + 20331 * q^61 + 32122 * q^62 + 19104 * q^63 + 31835 * q^64 + 13066 * q^65 + 17599 * q^66 + 1578 * q^67 - 2046 * q^68 - 14476 * q^69 - 7014 * q^70 - 17295 * q^71 - 39521 * q^72 - 12539 * q^73 - 19146 * q^74 - 35228 * q^75 - 43946 * q^76 - 6768 * q^77 - 31330 * q^78 - 11081 * q^79 - 12562 * q^80 + 6132 * q^81 + 12369 * q^82 + 16804 * q^83 + 31344 * q^84 + 13875 * q^85 + 16607 * q^86 + 17226 * q^87 + 22609 * q^88 + 11318 * q^89 + 21840 * q^90 + 1506 * q^91 + 20724 * q^92 - 10563 * q^93 - 10424 * q^94 - 21501 * q^95 - 39774 * q^96 - 21392 * q^97 - 55116 * q^98 - 14837 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(539))\)

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
539.4.a	\(\chi_{539}(1, \cdot)\)	539.4.a.a	1	1
		539.4.a.b	1
		539.4.a.c	1
		539.4.a.d	2
		539.4.a.e	2
		539.4.a.f	4
		539.4.a.g	4
		539.4.a.h	5
		539.4.a.i	6
		539.4.a.j	9
		539.4.a.k	9
		539.4.a.l	10
		539.4.a.m	10
		539.4.a.n	10
		539.4.a.o	10
		539.4.a.p	18
539.4.b	\(\chi_{539}(538, \cdot)\)	n/a	116	1
539.4.e	\(\chi_{539}(67, \cdot)\)	n/a	200	2
539.4.f	\(\chi_{539}(148, \cdot)\)	n/a	472	4
539.4.i	\(\chi_{539}(362, \cdot)\)	n/a	232	2
539.4.j	\(\chi_{539}(78, \cdot)\)	n/a	840	6
539.4.m	\(\chi_{539}(195, \cdot)\)	n/a	464	4
539.4.p	\(\chi_{539}(76, \cdot)\)	n/a	996	6
539.4.q	\(\chi_{539}(214, \cdot)\)	n/a	928	8
539.4.r	\(\chi_{539}(23, \cdot)\)	n/a	1680	12
539.4.s	\(\chi_{539}(19, \cdot)\)	n/a	928	8
539.4.v	\(\chi_{539}(15, \cdot)\)	n/a	3984	24
539.4.w	\(\chi_{539}(10, \cdot)\)	n/a	1992	12
539.4.z	\(\chi_{539}(6, \cdot)\)	n/a	3984	24
539.4.bc	\(\chi_{539}(4, \cdot)\)	n/a	7968	48
539.4.bf	\(\chi_{539}(17, \cdot)\)	n/a	7968	48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(539))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(539)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)