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Properties

Label 300.4
Level 300
Weight 4
Dimension 2863
Nonzero newspaces 12
Sturm bound 19200
Trace bound 6

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Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(19200\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(300))\).

Total New Old
Modular forms 7480 2947 4533
Cusp forms 6920 2863 4057
Eisenstein series 560 84 476

Trace form

\( 2863 q + 11 q^{3} - 12 q^{4} + 38 q^{5} - 10 q^{6} - 56 q^{7} - 168 q^{8} - 43 q^{9} + O(q^{10}) \) \( 2863 q + 11 q^{3} - 12 q^{4} + 38 q^{5} - 10 q^{6} - 56 q^{7} - 168 q^{8} - 43 q^{9} - 160 q^{10} - 76 q^{11} - 42 q^{12} + 262 q^{13} + 4 q^{15} + 508 q^{16} + 18 q^{17} + 198 q^{18} - 260 q^{19} + 380 q^{20} - 452 q^{21} + 812 q^{22} - 568 q^{23} + 220 q^{24} - 1166 q^{25} - 736 q^{26} + 611 q^{27} - 2036 q^{28} + 302 q^{29} - 86 q^{30} + 480 q^{31} - 680 q^{32} + 1784 q^{33} + 892 q^{34} + 1784 q^{35} - 186 q^{36} + 208 q^{37} - 916 q^{38} - 2470 q^{39} - 1736 q^{40} + 554 q^{41} + 346 q^{42} - 2076 q^{43} + 2660 q^{44} + 462 q^{45} + 4 q^{46} + 1472 q^{47} + 4060 q^{48} + 3019 q^{49} + 5636 q^{50} + 106 q^{51} + 1480 q^{52} + 2000 q^{53} + 1544 q^{54} + 3688 q^{55} + 3784 q^{56} + 4264 q^{57} + 664 q^{58} + 292 q^{59} - 6366 q^{60} - 26 q^{61} - 7356 q^{62} - 2356 q^{63} - 12000 q^{64} - 4710 q^{65} - 5794 q^{66} - 4292 q^{67} - 8864 q^{68} - 3044 q^{69} - 5052 q^{70} - 3720 q^{71} + 734 q^{72} - 2614 q^{73} + 1428 q^{75} - 648 q^{76} + 2496 q^{77} + 4728 q^{78} - 2096 q^{79} + 4636 q^{80} + 5093 q^{81} + 23916 q^{82} - 668 q^{83} + 20518 q^{84} - 4506 q^{85} + 10856 q^{86} + 6198 q^{87} + 14924 q^{88} - 440 q^{89} + 3470 q^{90} + 12896 q^{91} - 2824 q^{92} + 13108 q^{93} - 7972 q^{94} + 6320 q^{95} + 626 q^{96} + 17818 q^{97} - 20584 q^{98} - 1692 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(300))\)

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
300.4.a \(\chi_{300}(1, \cdot)\) 300.4.a.a 1 1
300.4.a.b 1
300.4.a.c 1
300.4.a.d 1
300.4.a.e 1
300.4.a.f 1
300.4.a.g 1
300.4.a.h 1
300.4.a.i 1
300.4.d \(\chi_{300}(49, \cdot)\) 300.4.d.a 2 1
300.4.d.b 2
300.4.d.c 2
300.4.d.d 2
300.4.d.e 2
300.4.e \(\chi_{300}(251, \cdot)\) n/a 108 1
300.4.h \(\chi_{300}(299, \cdot)\) n/a 104 1
300.4.i \(\chi_{300}(257, \cdot)\) 300.4.i.a 4 2
300.4.i.b 4
300.4.i.c 4
300.4.i.d 8
300.4.i.e 8
300.4.i.f 8
300.4.j \(\chi_{300}(7, \cdot)\) n/a 108 2
300.4.m \(\chi_{300}(61, \cdot)\) 300.4.m.a 32 4
300.4.m.b 32
300.4.n \(\chi_{300}(11, \cdot)\) n/a 704 4
300.4.o \(\chi_{300}(109, \cdot)\) 300.4.o.a 56 4
300.4.r \(\chi_{300}(59, \cdot)\) n/a 704 4
300.4.w \(\chi_{300}(67, \cdot)\) n/a 720 8
300.4.x \(\chi_{300}(17, \cdot)\) n/a 240 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(300)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 1}\)