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Properties

Label 3725.2
Level 3725
Weight 2
Dimension 508467
Nonzero newspaces 24
Sturm bound 2220000
Trace bound 3

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Defining parameters

Level: \( N \) = \( 3725 = 5^{2} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(2220000\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3725))\).

Total New Old
Modular forms 559144 514493 44651
Cusp forms 550857 508467 42390
Eisenstein series 8287 6026 2261

Trace form

\( 508467 q - 948 q^{2} - 950 q^{3} - 956 q^{4} - 1174 q^{5} - 1542 q^{6} - 958 q^{7} - 972 q^{8} - 968 q^{9} + O(q^{10}) \) \( 508467 q - 948 q^{2} - 950 q^{3} - 956 q^{4} - 1174 q^{5} - 1542 q^{6} - 958 q^{7} - 972 q^{8} - 968 q^{9} - 1194 q^{10} - 1542 q^{11} - 998 q^{12} - 970 q^{13} - 990 q^{14} - 1204 q^{15} - 1548 q^{16} - 958 q^{17} - 970 q^{18} - 942 q^{19} - 1164 q^{20} - 1542 q^{21} - 934 q^{22} - 950 q^{23} - 922 q^{24} - 1154 q^{25} - 3022 q^{26} - 962 q^{27} - 934 q^{28} - 962 q^{29} - 1204 q^{30} - 1542 q^{31} - 998 q^{32} - 998 q^{33} - 1000 q^{34} - 1224 q^{35} - 1588 q^{36} - 1008 q^{37} - 1002 q^{38} - 974 q^{39} - 1214 q^{40} - 1562 q^{41} - 934 q^{42} - 950 q^{43} - 970 q^{44} - 1134 q^{45} - 1542 q^{46} - 958 q^{47} - 890 q^{48} - 946 q^{49} - 1134 q^{50} - 3002 q^{51} - 918 q^{52} - 960 q^{53} - 922 q^{54} - 1204 q^{55} - 1574 q^{56} - 942 q^{57} - 982 q^{58} - 962 q^{59} - 1164 q^{60} - 1562 q^{61} - 914 q^{62} - 970 q^{63} - 976 q^{64} - 1194 q^{65} - 1590 q^{66} - 998 q^{67} - 954 q^{68} - 994 q^{69} - 1244 q^{70} - 1582 q^{71} - 992 q^{72} - 1010 q^{73} - 950 q^{74} - 1204 q^{75} - 3034 q^{76} - 974 q^{77} - 1018 q^{78} - 1022 q^{79} - 1194 q^{80} - 1608 q^{81} - 954 q^{82} - 890 q^{83} - 990 q^{84} - 1114 q^{85} - 1542 q^{86} - 922 q^{87} - 902 q^{88} - 872 q^{89} - 1134 q^{90} - 1542 q^{91} - 998 q^{92} - 938 q^{93} - 910 q^{94} - 1204 q^{95} - 1582 q^{96} - 858 q^{97} - 964 q^{98} - 994 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3725))\)

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
3725.2.a \(\chi_{3725}(1, \cdot)\) 3725.2.a.a 2 1
3725.2.a.b 3
3725.2.a.c 9
3725.2.a.d 10
3725.2.a.e 11
3725.2.a.f 12
3725.2.a.g 14
3725.2.a.h 25
3725.2.a.i 25
3725.2.a.j 25
3725.2.a.k 25
3725.2.a.l 30
3725.2.a.m 44
3725.2.b \(\chi_{3725}(299, \cdot)\) n/a 222 1
3725.2.c \(\chi_{3725}(3426, \cdot)\) n/a 234 1
3725.2.d \(\chi_{3725}(3724, \cdot)\) n/a 224 1
3725.2.e \(\chi_{3725}(193, \cdot)\) n/a 446 2
3725.2.j \(\chi_{3725}(1832, \cdot)\) n/a 446 2
3725.2.k \(\chi_{3725}(746, \cdot)\) n/a 1480 4
3725.2.l \(\chi_{3725}(744, \cdot)\) n/a 1488 4
3725.2.m \(\chi_{3725}(1044, \cdot)\) n/a 1480 4
3725.2.n \(\chi_{3725}(446, \cdot)\) n/a 1496 4
3725.2.o \(\chi_{3725}(342, \cdot)\) n/a 2984 8
3725.2.t \(\chi_{3725}(552, \cdot)\) n/a 2984 8
3725.2.u \(\chi_{3725}(251, \cdot)\) n/a 8460 36
3725.2.v \(\chi_{3725}(24, \cdot)\) n/a 8064 36
3725.2.w \(\chi_{3725}(26, \cdot)\) n/a 8424 36
3725.2.x \(\chi_{3725}(49, \cdot)\) n/a 7992 36
3725.2.y \(\chi_{3725}(43, \cdot)\) n/a 16056 72
3725.2.bd \(\chi_{3725}(18, \cdot)\) n/a 16056 72
3725.2.be \(\chi_{3725}(6, \cdot)\) n/a 53568 144
3725.2.bf \(\chi_{3725}(61, \cdot)\) n/a 53856 144
3725.2.bg \(\chi_{3725}(19, \cdot)\) n/a 53856 144
3725.2.bh \(\chi_{3725}(4, \cdot)\) n/a 53568 144
3725.2.bi \(\chi_{3725}(2, \cdot)\) n/a 107424 288
3725.2.bn \(\chi_{3725}(13, \cdot)\) n/a 107424 288

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3725))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3725)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(149))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(745))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3725))\)\(^{\oplus 1}\)