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Properties

Label 375.4
Level 375
Weight 4
Dimension 10240
Nonzero newspaces 9
Sturm bound 40000
Trace bound 4

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Defining parameters

Level: \( N \) = \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 9 \)
Sturm bound: \(40000\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(375))\).

Total New Old
Modular forms 15360 10496 4864
Cusp forms 14640 10240 4400
Eisenstein series 720 256 464

Trace form

\( 10240 q + 4 q^{2} - 36 q^{3} - 84 q^{4} - 54 q^{6} - 80 q^{7} - 36 q^{8} - 48 q^{9} + O(q^{10}) \) \( 10240 q + 4 q^{2} - 36 q^{3} - 84 q^{4} - 54 q^{6} - 80 q^{7} - 36 q^{8} - 48 q^{9} - 80 q^{10} - 56 q^{11} + 78 q^{12} + 104 q^{13} + 264 q^{14} - 40 q^{15} - 828 q^{16} - 1240 q^{17} - 594 q^{18} - 796 q^{19} + 280 q^{20} - 162 q^{21} + 2300 q^{22} + 1472 q^{23} + 2542 q^{24} + 1360 q^{25} + 1992 q^{26} + 672 q^{27} + 3516 q^{28} + 1108 q^{29} - 280 q^{30} - 916 q^{31} - 4364 q^{32} - 1962 q^{33} - 7228 q^{34} - 1720 q^{35} - 1774 q^{36} - 3460 q^{37} - 10352 q^{38} - 5534 q^{39} - 4180 q^{40} - 2204 q^{41} - 1142 q^{42} + 1512 q^{43} + 6048 q^{44} + 2280 q^{45} + 9164 q^{46} + 7112 q^{47} + 11570 q^{48} + 8870 q^{49} + 8820 q^{50} + 5122 q^{51} + 15244 q^{52} + 6772 q^{53} + 7294 q^{54} + 1440 q^{55} + 1680 q^{56} - 154 q^{57} - 6444 q^{58} - 6064 q^{59} - 700 q^{60} - 5632 q^{61} - 21088 q^{62} - 3478 q^{63} - 18156 q^{64} - 1910 q^{65} - 2454 q^{66} + 64 q^{67} + 152 q^{68} - 6046 q^{69} - 80 q^{70} - 688 q^{71} - 21194 q^{72} - 3040 q^{73} - 3376 q^{74} - 5960 q^{75} - 6116 q^{76} - 1728 q^{77} - 13930 q^{78} - 1580 q^{79} - 1840 q^{81} - 29268 q^{82} - 26312 q^{83} - 16254 q^{84} - 16730 q^{85} - 15536 q^{86} - 1706 q^{87} - 13716 q^{88} - 4176 q^{89} + 10460 q^{90} + 10124 q^{91} + 18256 q^{92} + 20954 q^{93} + 47516 q^{94} + 12640 q^{95} + 23986 q^{96} + 54504 q^{97} + 54724 q^{98} + 958 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(375))\)

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
375.4.a \(\chi_{375}(1, \cdot)\) 375.4.a.a 4 1
375.4.a.b 4
375.4.a.c 6
375.4.a.d 6
375.4.a.e 6
375.4.a.f 6
375.4.a.g 8
375.4.a.h 8
375.4.b \(\chi_{375}(124, \cdot)\) 375.4.b.a 8 1
375.4.b.b 12
375.4.b.c 12
375.4.b.d 16
375.4.e \(\chi_{375}(68, \cdot)\) n/a 192 2
375.4.g \(\chi_{375}(76, \cdot)\) n/a 184 4
375.4.i \(\chi_{375}(49, \cdot)\) n/a 176 4
375.4.l \(\chi_{375}(32, \cdot)\) n/a 672 8
375.4.m \(\chi_{375}(16, \cdot)\) n/a 1480 20
375.4.o \(\chi_{375}(4, \cdot)\) n/a 1520 20
375.4.r \(\chi_{375}(2, \cdot)\) n/a 5920 40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(375))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(375)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 2}\)