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Properties

Label 525.6
Level 525
Weight 6
Dimension 31592
Nonzero newspaces 24
Sturm bound 115200
Trace bound 4

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Defining parameters

Level: \( N \) = \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(115200\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(525))\).

Total New Old
Modular forms 48672 32004 16668
Cusp forms 47328 31592 15736
Eisenstein series 1344 412 932

Trace form

\( 31592 q - 20 q^{2} - 28 q^{3} + 210 q^{4} + 252 q^{5} - 756 q^{6} - 570 q^{7} + 438 q^{8} - 184 q^{9} + O(q^{10}) \) \( 31592 q - 20 q^{2} - 28 q^{3} + 210 q^{4} + 252 q^{5} - 756 q^{6} - 570 q^{7} + 438 q^{8} - 184 q^{9} + 3472 q^{10} + 874 q^{11} + 536 q^{12} - 4474 q^{13} - 7512 q^{14} - 6868 q^{15} - 6462 q^{16} + 5024 q^{17} + 21338 q^{18} + 46982 q^{19} + 47688 q^{20} - 2364 q^{21} - 37400 q^{22} - 48520 q^{23} - 59388 q^{24} - 92548 q^{25} - 10614 q^{26} + 10010 q^{27} + 204934 q^{28} + 176608 q^{29} + 63212 q^{30} - 66378 q^{31} - 144050 q^{32} - 126028 q^{33} - 340332 q^{34} - 122612 q^{35} + 185030 q^{36} + 115180 q^{37} + 32110 q^{38} + 175314 q^{39} + 515056 q^{40} + 207220 q^{41} + 285192 q^{42} + 208424 q^{43} + 113856 q^{44} - 92252 q^{45} - 835836 q^{46} - 747010 q^{47} - 657956 q^{48} - 157626 q^{49} - 659992 q^{50} + 470192 q^{51} + 699504 q^{52} + 260008 q^{53} + 302262 q^{54} - 3032 q^{55} - 390342 q^{56} + 62284 q^{57} + 1149120 q^{58} + 853244 q^{59} + 1114724 q^{60} + 371402 q^{61} + 637436 q^{62} - 306166 q^{63} - 748058 q^{64} - 308828 q^{65} - 499974 q^{66} - 1146950 q^{67} - 1253248 q^{68} - 168572 q^{69} - 1484476 q^{70} - 975892 q^{71} + 58470 q^{72} - 1429516 q^{73} - 777130 q^{74} + 443124 q^{75} + 960200 q^{76} + 1347360 q^{77} + 3131824 q^{78} + 3269774 q^{79} + 2057152 q^{80} + 1221116 q^{81} + 1203448 q^{82} - 411380 q^{83} - 1451198 q^{84} + 420436 q^{85} - 2098922 q^{86} - 1184280 q^{87} - 259124 q^{88} + 852852 q^{89} - 78844 q^{90} - 102076 q^{91} + 1231120 q^{92} - 254714 q^{93} - 1294440 q^{94} - 1245872 q^{95} + 464196 q^{96} - 2494868 q^{97} - 1517658 q^{98} + 872220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(525))\)

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
525.6.a \(\chi_{525}(1, \cdot)\) 525.6.a.a 1 1
525.6.a.b 1
525.6.a.c 1
525.6.a.d 1
525.6.a.e 2
525.6.a.f 2
525.6.a.g 2
525.6.a.h 2
525.6.a.i 2
525.6.a.j 2
525.6.a.k 4
525.6.a.l 4
525.6.a.m 4
525.6.a.n 4
525.6.a.o 4
525.6.a.p 4
525.6.a.q 6
525.6.a.r 6
525.6.a.s 6
525.6.a.t 6
525.6.a.u 7
525.6.a.v 7
525.6.a.w 9
525.6.a.x 9
525.6.b \(\chi_{525}(251, \cdot)\) n/a 248 1
525.6.d \(\chi_{525}(274, \cdot)\) 525.6.d.a 2 1
525.6.d.b 2
525.6.d.c 2
525.6.d.d 2
525.6.d.e 4
525.6.d.f 4
525.6.d.g 4
525.6.d.h 4
525.6.d.i 4
525.6.d.j 4
525.6.d.k 8
525.6.d.l 8
525.6.d.m 8
525.6.d.n 8
525.6.d.o 12
525.6.d.p 12
525.6.g \(\chi_{525}(524, \cdot)\) n/a 236 1
525.6.i \(\chi_{525}(151, \cdot)\) n/a 254 2
525.6.j \(\chi_{525}(218, \cdot)\) n/a 360 2
525.6.m \(\chi_{525}(118, \cdot)\) n/a 240 2
525.6.n \(\chi_{525}(106, \cdot)\) n/a 592 4
525.6.q \(\chi_{525}(299, \cdot)\) n/a 472 2
525.6.r \(\chi_{525}(424, \cdot)\) n/a 240 2
525.6.t \(\chi_{525}(26, \cdot)\) n/a 494 2
525.6.w \(\chi_{525}(104, \cdot)\) n/a 1584 4
525.6.z \(\chi_{525}(64, \cdot)\) n/a 608 4
525.6.bb \(\chi_{525}(41, \cdot)\) n/a 1584 4
525.6.bc \(\chi_{525}(82, \cdot)\) n/a 480 4
525.6.bf \(\chi_{525}(32, \cdot)\) n/a 944 4
525.6.bg \(\chi_{525}(16, \cdot)\) n/a 1600 8
525.6.bh \(\chi_{525}(13, \cdot)\) n/a 1600 8
525.6.bk \(\chi_{525}(8, \cdot)\) n/a 2400 8
525.6.bm \(\chi_{525}(131, \cdot)\) n/a 3168 8
525.6.bo \(\chi_{525}(4, \cdot)\) n/a 1600 8
525.6.bp \(\chi_{525}(59, \cdot)\) n/a 3168 8
525.6.bs \(\chi_{525}(2, \cdot)\) n/a 6336 16
525.6.bv \(\chi_{525}(52, \cdot)\) n/a 3200 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(525))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(525)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)