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Properties

Label 2025.4
Level 2025
Weight 4
Dimension 317380
Nonzero newspaces 24
Sturm bound 1166400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2025 = 3^{4} \cdot 5^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(1166400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2025))\).

Total New Old
Modular forms 440424 319676 120748
Cusp forms 434376 317380 116996
Eisenstein series 6048 2296 3752

Trace form

\( 317380 q - 156 q^{2} - 234 q^{3} - 268 q^{4} - 192 q^{5} - 378 q^{6} - 242 q^{7} - 87 q^{8} - 234 q^{9} + O(q^{10}) \) \( 317380 q - 156 q^{2} - 234 q^{3} - 268 q^{4} - 192 q^{5} - 378 q^{6} - 242 q^{7} - 87 q^{8} - 234 q^{9} - 464 q^{10} - 315 q^{11} - 234 q^{12} - 314 q^{13} - 213 q^{14} - 288 q^{15} - 248 q^{16} + 45 q^{17} + 180 q^{18} + 73 q^{19} - 192 q^{20} - 270 q^{21} - 438 q^{22} - 942 q^{23} - 1314 q^{24} - 320 q^{25} - 3807 q^{26} - 936 q^{27} - 1797 q^{28} - 1182 q^{29} - 288 q^{30} - 366 q^{31} + 2238 q^{32} + 198 q^{33} + 3792 q^{34} + 1464 q^{35} + 1926 q^{36} + 1729 q^{37} + 2028 q^{38} - 234 q^{39} - 2048 q^{40} + 255 q^{41} + 3321 q^{42} - 2843 q^{43} - 5823 q^{44} - 288 q^{45} - 4837 q^{46} - 6300 q^{47} - 2511 q^{48} - 4365 q^{49} - 1536 q^{50} - 3699 q^{51} - 2609 q^{52} - 2391 q^{53} - 6912 q^{54} + 1120 q^{55} + 657 q^{56} - 2448 q^{57} + 2993 q^{58} + 135 q^{59} - 288 q^{60} - 456 q^{61} + 3837 q^{62} + 1764 q^{63} + 6381 q^{64} - 192 q^{65} - 2322 q^{66} + 6193 q^{67} + 10032 q^{68} - 612 q^{69} + 680 q^{70} + 2127 q^{71} + 1494 q^{72} + 8047 q^{73} + 27135 q^{74} - 288 q^{75} + 7946 q^{76} + 17772 q^{77} + 10665 q^{78} - 1160 q^{79} - 12 q^{80} + 5382 q^{81} - 10806 q^{82} - 9582 q^{83} + 17145 q^{84} - 5288 q^{85} - 29946 q^{86} + 5238 q^{87} - 23332 q^{88} - 13503 q^{89} - 288 q^{90} - 7577 q^{91} - 18627 q^{92} + 3564 q^{93} - 6783 q^{94} - 7272 q^{95} - 17613 q^{96} + 163 q^{97} - 22701 q^{98} - 13446 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2025))\)

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
2025.4.a \(\chi_{2025}(1, \cdot)\) 2025.4.a.a 1 1
2025.4.a.b 1
2025.4.a.c 1
2025.4.a.d 1
2025.4.a.e 1
2025.4.a.f 1
2025.4.a.g 2
2025.4.a.h 2
2025.4.a.i 2
2025.4.a.j 2
2025.4.a.k 2
2025.4.a.l 2
2025.4.a.m 2
2025.4.a.n 2
2025.4.a.o 2
2025.4.a.p 3
2025.4.a.q 3
2025.4.a.r 3
2025.4.a.s 3
2025.4.a.t 4
2025.4.a.u 5
2025.4.a.v 5
2025.4.a.w 5
2025.4.a.x 5
2025.4.a.y 6
2025.4.a.z 6
2025.4.a.ba 7
2025.4.a.bb 7
2025.4.a.bc 8
2025.4.a.bd 8
2025.4.a.be 12
2025.4.a.bf 12
2025.4.a.bg 12
2025.4.a.bh 12
2025.4.a.bi 12
2025.4.a.bj 12
2025.4.a.bk 16
2025.4.a.bl 16
2025.4.a.bm 16
2025.4.b \(\chi_{2025}(649, \cdot)\) n/a 212 1
2025.4.e \(\chi_{2025}(676, \cdot)\) n/a 450 2
2025.4.f \(\chi_{2025}(1457, \cdot)\) n/a 424 2
2025.4.h \(\chi_{2025}(406, \cdot)\) n/a 1424 4
2025.4.k \(\chi_{2025}(1324, \cdot)\) n/a 428 2
2025.4.l \(\chi_{2025}(226, \cdot)\) n/a 1008 6
2025.4.n \(\chi_{2025}(244, \cdot)\) n/a 1424 4
2025.4.q \(\chi_{2025}(107, \cdot)\) n/a 856 4
2025.4.r \(\chi_{2025}(136, \cdot)\) n/a 2864 8
2025.4.u \(\chi_{2025}(199, \cdot)\) n/a 960 6
2025.4.w \(\chi_{2025}(242, \cdot)\) n/a 2848 8
2025.4.x \(\chi_{2025}(76, \cdot)\) n/a 9180 18
2025.4.z \(\chi_{2025}(109, \cdot)\) n/a 2864 8
2025.4.bb \(\chi_{2025}(143, \cdot)\) n/a 1920 12
2025.4.bd \(\chi_{2025}(46, \cdot)\) n/a 6432 24
2025.4.be \(\chi_{2025}(49, \cdot)\) n/a 8712 18
2025.4.bh \(\chi_{2025}(53, \cdot)\) n/a 5728 16
2025.4.bk \(\chi_{2025}(19, \cdot)\) n/a 6432 24
2025.4.bn \(\chi_{2025}(32, \cdot)\) n/a 17424 36
2025.4.bo \(\chi_{2025}(16, \cdot)\) n/a 58176 72
2025.4.bp \(\chi_{2025}(8, \cdot)\) n/a 12864 48
2025.4.br \(\chi_{2025}(4, \cdot)\) n/a 58176 72
2025.4.bv \(\chi_{2025}(2, \cdot)\) n/a 116352 144

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2025))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2025)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 2}\)