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Properties

Label 725.4
Level 725
Weight 4
Dimension 57373
Nonzero newspaces 24
Sturm bound 168000
Trace bound 3

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Defining parameters

Level: \( N \) = \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(168000\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(725))\).

Total New Old
Modular forms 63784 58479 5305
Cusp forms 62216 57373 4843
Eisenstein series 1568 1106 462

Trace form

\( 57373 q - 178 q^{2} - 154 q^{3} - 130 q^{4} - 214 q^{5} - 290 q^{6} - 138 q^{7} - 162 q^{8} - 254 q^{9} + O(q^{10}) \) \( 57373 q - 178 q^{2} - 154 q^{3} - 130 q^{4} - 214 q^{5} - 290 q^{6} - 138 q^{7} - 162 q^{8} - 254 q^{9} - 164 q^{10} - 130 q^{11} - 98 q^{12} - 314 q^{13} - 258 q^{14} - 224 q^{15} - 2 q^{16} + 582 q^{17} + 1106 q^{18} + 478 q^{19} - 564 q^{20} - 1474 q^{21} - 2506 q^{22} - 1382 q^{23} - 2350 q^{24} - 1594 q^{25} - 20 q^{26} - 550 q^{27} + 144 q^{28} + 432 q^{29} + 132 q^{30} + 646 q^{31} + 3998 q^{32} + 2350 q^{33} + 2652 q^{34} + 1456 q^{35} - 594 q^{36} + 1356 q^{37} + 1482 q^{38} + 2118 q^{39} + 3896 q^{40} + 750 q^{41} + 1046 q^{42} + 1046 q^{43} - 3548 q^{44} - 4614 q^{45} - 8700 q^{46} - 7142 q^{47} - 16430 q^{48} - 6620 q^{49} - 9224 q^{50} - 5110 q^{51} - 5934 q^{52} - 1153 q^{53} - 432 q^{54} - 2044 q^{55} + 5204 q^{56} + 4936 q^{57} + 11414 q^{58} + 9796 q^{59} + 22716 q^{60} + 7830 q^{61} + 25732 q^{62} + 18750 q^{63} + 15100 q^{64} + 3686 q^{65} + 254 q^{66} - 2946 q^{67} - 12204 q^{68} - 11146 q^{69} - 8604 q^{70} - 13538 q^{71} - 39788 q^{72} - 18527 q^{73} - 28088 q^{74} - 11944 q^{75} - 10502 q^{76} - 10554 q^{77} - 9238 q^{78} - 1242 q^{79} - 11884 q^{80} + 10970 q^{81} + 16862 q^{82} + 18670 q^{83} + 39684 q^{84} + 19066 q^{85} + 21616 q^{86} + 14308 q^{87} + 38968 q^{88} + 20088 q^{89} + 16096 q^{90} + 7974 q^{91} + 16710 q^{92} - 6882 q^{93} - 12338 q^{94} - 13844 q^{95} - 21764 q^{96} - 36453 q^{97} - 40772 q^{98} - 49330 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(725))\)

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
725.4.a \(\chi_{725}(1, \cdot)\) 725.4.a.a 1 1
725.4.a.b 2
725.4.a.c 5
725.4.a.d 6
725.4.a.e 6
725.4.a.f 7
725.4.a.g 8
725.4.a.h 14
725.4.a.i 14
725.4.a.j 14
725.4.a.k 14
725.4.a.l 18
725.4.a.m 24
725.4.b \(\chi_{725}(349, \cdot)\) n/a 126 1
725.4.c \(\chi_{725}(376, \cdot)\) n/a 140 1
725.4.d \(\chi_{725}(724, \cdot)\) n/a 132 1
725.4.e \(\chi_{725}(157, \cdot)\) n/a 266 2
725.4.j \(\chi_{725}(307, \cdot)\) n/a 266 2
725.4.k \(\chi_{725}(146, \cdot)\) n/a 840 4
725.4.l \(\chi_{725}(226, \cdot)\) n/a 834 6
725.4.m \(\chi_{725}(144, \cdot)\) n/a 896 4
725.4.n \(\chi_{725}(59, \cdot)\) n/a 840 4
725.4.o \(\chi_{725}(86, \cdot)\) n/a 888 4
725.4.p \(\chi_{725}(149, \cdot)\) n/a 792 6
725.4.q \(\chi_{725}(51, \cdot)\) n/a 840 6
725.4.r \(\chi_{725}(24, \cdot)\) n/a 804 6
725.4.s \(\chi_{725}(17, \cdot)\) n/a 1784 8
725.4.x \(\chi_{725}(12, \cdot)\) n/a 1784 8
725.4.y \(\chi_{725}(18, \cdot)\) n/a 1596 12
725.4.bd \(\chi_{725}(43, \cdot)\) n/a 1596 12
725.4.be \(\chi_{725}(16, \cdot)\) n/a 5376 24
725.4.bf \(\chi_{725}(6, \cdot)\) n/a 5328 24
725.4.bg \(\chi_{725}(54, \cdot)\) n/a 5328 24
725.4.bh \(\chi_{725}(4, \cdot)\) n/a 5376 24
725.4.bi \(\chi_{725}(3, \cdot)\) n/a 10704 48
725.4.bn \(\chi_{725}(2, \cdot)\) n/a 10704 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(725))\) into lower level spaces

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