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Properties

Label 725.6
Level 725
Weight 6
Dimension 95991
Nonzero newspaces 24
Sturm bound 252000
Trace bound 3

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Defining parameters

Level: \( N \) = \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(252000\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(725))\).

Total New Old
Modular forms 105784 97097 8687
Cusp forms 104216 95991 8225
Eisenstein series 1568 1106 462

Trace form

\( 95991 q - 154 q^{2} - 178 q^{3} - 370 q^{4} - 334 q^{5} + 766 q^{6} + 606 q^{7} - 642 q^{8} - 2294 q^{9} + O(q^{10}) \) \( 95991 q - 154 q^{2} - 178 q^{3} - 370 q^{4} - 334 q^{5} + 766 q^{6} + 606 q^{7} - 642 q^{8} - 2294 q^{9} - 984 q^{10} + 1166 q^{11} + 286 q^{12} + 982 q^{13} + 4542 q^{14} + 2236 q^{15} + 446 q^{16} - 3054 q^{17} - 18178 q^{18} - 15242 q^{19} - 20724 q^{20} - 7774 q^{21} + 34222 q^{22} + 38176 q^{23} + 118898 q^{24} + 37806 q^{25} + 10006 q^{26} - 15040 q^{27} - 102064 q^{28} - 70032 q^{29} - 108108 q^{30} - 9574 q^{31} - 36898 q^{32} + 19408 q^{33} + 113522 q^{34} + 80536 q^{35} + 246126 q^{36} + 76630 q^{37} + 144546 q^{38} - 94206 q^{39} - 179704 q^{40} - 123234 q^{41} - 408106 q^{42} - 125058 q^{43} - 225884 q^{44} + 35346 q^{45} + 4836 q^{46} + 137314 q^{47} + 865330 q^{48} + 565136 q^{49} + 504676 q^{50} + 247322 q^{51} + 280978 q^{52} + 109289 q^{53} - 216336 q^{54} - 182484 q^{55} - 627484 q^{56} - 774920 q^{57} - 841730 q^{58} - 407696 q^{59} - 195204 q^{60} + 3022 q^{61} - 169388 q^{62} - 750 q^{63} + 94556 q^{64} - 272554 q^{65} + 462158 q^{66} + 321222 q^{67} + 377076 q^{68} + 610730 q^{69} + 235076 q^{70} + 179392 q^{71} + 716932 q^{72} - 177025 q^{73} + 490960 q^{74} + 621356 q^{75} + 1485754 q^{76} + 950604 q^{77} + 1051898 q^{78} + 440226 q^{79} - 4204 q^{80} - 279886 q^{81} + 498430 q^{82} - 444302 q^{83} - 2619852 q^{84} - 1362554 q^{85} - 3023288 q^{86} - 1625792 q^{87} - 4243176 q^{88} - 1536282 q^{89} - 1509044 q^{90} - 311438 q^{91} + 1085574 q^{92} + 927042 q^{93} + 1520478 q^{94} + 847756 q^{95} + 1145212 q^{96} + 1164325 q^{97} + 3540436 q^{98} + 3084044 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(725))\)

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
725.6.a \(\chi_{725}(1, \cdot)\) 725.6.a.a 4 1
725.6.a.b 7
725.6.a.c 11
725.6.a.d 11
725.6.a.e 13
725.6.a.f 13
725.6.a.g 23
725.6.a.h 23
725.6.a.i 23
725.6.a.j 23
725.6.a.k 32
725.6.a.l 38
725.6.b \(\chi_{725}(349, \cdot)\) n/a 210 1
725.6.c \(\chi_{725}(376, \cdot)\) n/a 234 1
725.6.d \(\chi_{725}(724, \cdot)\) n/a 224 1
725.6.e \(\chi_{725}(157, \cdot)\) n/a 446 2
725.6.j \(\chi_{725}(307, \cdot)\) n/a 446 2
725.6.k \(\chi_{725}(146, \cdot)\) n/a 1400 4
725.6.l \(\chi_{725}(226, \cdot)\) n/a 1410 6
725.6.m \(\chi_{725}(144, \cdot)\) n/a 1488 4
725.6.n \(\chi_{725}(59, \cdot)\) n/a 1400 4
725.6.o \(\chi_{725}(86, \cdot)\) n/a 1496 4
725.6.p \(\chi_{725}(149, \cdot)\) n/a 1344 6
725.6.q \(\chi_{725}(51, \cdot)\) n/a 1404 6
725.6.r \(\chi_{725}(24, \cdot)\) n/a 1332 6
725.6.s \(\chi_{725}(17, \cdot)\) n/a 2984 8
725.6.x \(\chi_{725}(12, \cdot)\) n/a 2984 8
725.6.y \(\chi_{725}(18, \cdot)\) n/a 2676 12
725.6.bd \(\chi_{725}(43, \cdot)\) n/a 2676 12
725.6.be \(\chi_{725}(16, \cdot)\) n/a 8928 24
725.6.bf \(\chi_{725}(6, \cdot)\) n/a 8976 24
725.6.bg \(\chi_{725}(54, \cdot)\) n/a 8976 24
725.6.bh \(\chi_{725}(4, \cdot)\) n/a 8928 24
725.6.bi \(\chi_{725}(3, \cdot)\) n/a 17904 48
725.6.bn \(\chi_{725}(2, \cdot)\) n/a 17904 48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(725))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(725)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 2}\)