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Properties

Label 300.5
Level 300
Weight 5
Dimension 3829
Nonzero newspaces 12
Sturm bound 24000
Trace bound 7

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Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(24000\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(300))\).

Total New Old
Modular forms 9880 3909 5971
Cusp forms 9320 3829 5491
Eisenstein series 560 80 480

Trace form

\( 3829 q + 6 q^{2} - 11 q^{3} - 40 q^{4} - 12 q^{5} + 44 q^{6} + 346 q^{7} + 360 q^{8} - 327 q^{9} + O(q^{10}) \) \( 3829 q + 6 q^{2} - 11 q^{3} - 40 q^{4} - 12 q^{5} + 44 q^{6} + 346 q^{7} + 360 q^{8} - 327 q^{9} - 320 q^{10} - 576 q^{11} - 222 q^{12} - 1102 q^{13} - 120 q^{14} + 194 q^{15} - 212 q^{16} + 1740 q^{17} - 1084 q^{18} + 1514 q^{19} + 780 q^{20} - 638 q^{21} + 3188 q^{22} - 840 q^{23} + 1296 q^{24} - 3116 q^{25} + 2364 q^{26} - 1451 q^{27} - 1876 q^{28} + 1008 q^{29} + 1434 q^{30} - 3078 q^{31} - 6984 q^{32} + 2616 q^{33} - 14264 q^{34} + 9804 q^{35} + 4170 q^{36} + 4626 q^{37} + 18300 q^{38} + 13674 q^{39} + 3864 q^{40} + 6744 q^{41} - 13366 q^{42} - 8694 q^{43} - 12516 q^{44} - 18748 q^{45} + 12884 q^{46} - 24000 q^{47} - 10112 q^{48} - 17817 q^{49} + 9636 q^{50} - 5944 q^{51} + 7688 q^{52} + 19632 q^{53} + 54426 q^{54} + 18848 q^{55} - 11400 q^{56} + 13238 q^{57} + 22932 q^{58} + 14400 q^{59} + 3074 q^{60} + 35426 q^{61} - 4524 q^{62} - 18164 q^{63} + 17240 q^{64} + 14700 q^{65} + 5382 q^{66} + 23626 q^{67} + 8136 q^{68} - 11642 q^{69} - 24972 q^{70} + 7200 q^{71} - 20242 q^{72} - 74846 q^{73} - 112356 q^{74} - 2242 q^{75} - 87976 q^{76} - 47472 q^{77} - 49672 q^{78} - 78558 q^{79} - 9084 q^{80} - 67015 q^{81} - 113960 q^{82} + 32160 q^{83} - 24202 q^{84} + 70584 q^{85} + 100128 q^{86} - 38270 q^{87} + 169676 q^{88} - 73440 q^{89} + 55910 q^{90} - 24556 q^{91} + 74856 q^{92} - 71420 q^{93} + 167308 q^{94} - 18480 q^{95} + 34274 q^{96} - 26670 q^{97} + 24270 q^{98} + 133760 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(300))\)

We only show spaces with odd 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
300.5.b \(\chi_{300}(149, \cdot)\) 300.5.b.a 2 1
300.5.b.b 2
300.5.b.c 4
300.5.b.d 8
300.5.b.e 8
300.5.c \(\chi_{300}(151, \cdot)\) 300.5.c.a 4 1
300.5.c.b 16
300.5.c.c 16
300.5.c.d 16
300.5.c.e 24
300.5.f \(\chi_{300}(199, \cdot)\) 300.5.f.a 8 1
300.5.f.b 32
300.5.f.c 32
300.5.g \(\chi_{300}(101, \cdot)\) 300.5.g.a 1 1
300.5.g.b 1
300.5.g.c 1
300.5.g.d 2
300.5.g.e 4
300.5.g.f 4
300.5.g.g 4
300.5.g.h 8
300.5.k \(\chi_{300}(157, \cdot)\) 300.5.k.a 4 2
300.5.k.b 4
300.5.k.c 8
300.5.k.d 8
300.5.l \(\chi_{300}(107, \cdot)\) n/a 280 2
300.5.p \(\chi_{300}(31, \cdot)\) n/a 480 4
300.5.q \(\chi_{300}(29, \cdot)\) n/a 160 4
300.5.s \(\chi_{300}(41, \cdot)\) n/a 160 4
300.5.t \(\chi_{300}(19, \cdot)\) n/a 480 4
300.5.u \(\chi_{300}(23, \cdot)\) n/a 1888 8
300.5.v \(\chi_{300}(13, \cdot)\) n/a 160 8

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

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