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Properties

Label 325.4
Level 325
Weight 4
Dimension 11249
Nonzero newspaces 24
Sturm bound 33600
Trace bound 4

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Defining parameters

Level: \( N \) = \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(33600\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(325))\).

Total New Old
Modular forms 12936 11699 1237
Cusp forms 12264 11249 1015
Eisenstein series 672 450 222

Trace form

\( 11249 q - 74 q^{2} - 50 q^{3} - 26 q^{4} - 86 q^{5} - 122 q^{6} - 70 q^{7} - 130 q^{8} - 150 q^{9} + O(q^{10}) \) \( 11249 q - 74 q^{2} - 50 q^{3} - 26 q^{4} - 86 q^{5} - 122 q^{6} - 70 q^{7} - 130 q^{8} - 150 q^{9} - 36 q^{10} + 98 q^{11} + 240 q^{12} - 112 q^{14} - 96 q^{15} + 166 q^{16} + 497 q^{17} + 382 q^{18} + 138 q^{19} - 436 q^{20} - 522 q^{21} - 1620 q^{22} - 1022 q^{23} - 1862 q^{24} - 1466 q^{25} + 396 q^{26} - 788 q^{27} - 1360 q^{28} - 847 q^{29} + 484 q^{30} - 114 q^{31} + 2552 q^{32} + 1518 q^{33} + 2130 q^{34} + 1584 q^{35} + 1770 q^{36} + 2259 q^{37} + 4684 q^{38} + 2292 q^{39} + 3928 q^{40} + 447 q^{41} + 520 q^{42} + 730 q^{43} - 1460 q^{44} - 4486 q^{45} - 2454 q^{46} - 5422 q^{47} - 9942 q^{48} - 4704 q^{49} - 7344 q^{50} + 5316 q^{51} + 10660 q^{52} + 4018 q^{53} + 7976 q^{54} - 44 q^{55} + 3400 q^{56} + 1106 q^{57} + 236 q^{58} + 4138 q^{59} + 10172 q^{60} - 645 q^{61} + 2890 q^{62} - 8182 q^{63} - 14364 q^{64} - 4285 q^{65} - 25972 q^{66} - 13042 q^{67} - 24300 q^{68} - 19598 q^{69} - 13372 q^{70} - 3570 q^{71} - 20220 q^{72} - 6018 q^{73} - 10904 q^{74} - 6296 q^{75} + 10262 q^{76} + 3456 q^{77} + 31540 q^{78} + 11000 q^{79} + 3028 q^{80} + 25296 q^{81} + 22636 q^{82} + 18062 q^{83} + 39368 q^{84} + 19194 q^{85} + 6956 q^{86} + 12962 q^{87} + 24704 q^{88} + 10872 q^{89} + 16224 q^{90} - 1488 q^{91} + 2528 q^{92} - 13430 q^{93} - 15630 q^{94} - 13716 q^{95} - 8128 q^{96} - 22742 q^{97} - 24870 q^{98} - 21546 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(325))\)

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
325.4.a \(\chi_{325}(1, \cdot)\) 325.4.a.a 1 1
325.4.a.b 1
325.4.a.c 1
325.4.a.d 1
325.4.a.e 2
325.4.a.f 2
325.4.a.g 2
325.4.a.h 2
325.4.a.i 5
325.4.a.j 5
325.4.a.k 5
325.4.a.l 7
325.4.a.m 7
325.4.a.n 8
325.4.a.o 8
325.4.b \(\chi_{325}(274, \cdot)\) 325.4.b.a 2 1
325.4.b.b 2
325.4.b.c 4
325.4.b.d 4
325.4.b.e 4
325.4.b.f 4
325.4.b.g 10
325.4.b.h 10
325.4.b.i 14
325.4.c \(\chi_{325}(51, \cdot)\) 325.4.c.a 2 1
325.4.c.b 2
325.4.c.c 2
325.4.c.d 14
325.4.c.e 14
325.4.c.f 14
325.4.c.g 16
325.4.d \(\chi_{325}(324, \cdot)\) 325.4.d.a 2 1
325.4.d.b 2
325.4.d.c 14
325.4.d.d 14
325.4.d.e 28
325.4.e \(\chi_{325}(126, \cdot)\) n/a 126 2
325.4.f \(\chi_{325}(18, \cdot)\) n/a 122 2
325.4.k \(\chi_{325}(57, \cdot)\) n/a 122 2
325.4.l \(\chi_{325}(66, \cdot)\) n/a 360 4
325.4.m \(\chi_{325}(49, \cdot)\) n/a 120 2
325.4.n \(\chi_{325}(101, \cdot)\) n/a 128 2
325.4.o \(\chi_{325}(74, \cdot)\) n/a 124 2
325.4.p \(\chi_{325}(64, \cdot)\) n/a 416 4
325.4.q \(\chi_{325}(116, \cdot)\) n/a 408 4
325.4.r \(\chi_{325}(14, \cdot)\) n/a 360 4
325.4.s \(\chi_{325}(32, \cdot)\) n/a 244 4
325.4.x \(\chi_{325}(7, \cdot)\) n/a 244 4
325.4.y \(\chi_{325}(16, \cdot)\) n/a 832 8
325.4.z \(\chi_{325}(8, \cdot)\) n/a 824 8
325.4.be \(\chi_{325}(47, \cdot)\) n/a 824 8
325.4.bf \(\chi_{325}(9, \cdot)\) n/a 816 8
325.4.bg \(\chi_{325}(36, \cdot)\) n/a 816 8
325.4.bh \(\chi_{325}(4, \cdot)\) n/a 832 8
325.4.bi \(\chi_{325}(28, \cdot)\) n/a 1648 16
325.4.bn \(\chi_{325}(2, \cdot)\) n/a 1648 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(325))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(325)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)