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Properties

Label 300.9
Level 300
Weight 9
Dimension 7699
Nonzero newspaces 12
Sturm bound 43200
Trace bound 7

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Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(43200\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(300))\).

Total New Old
Modular forms 19480 7779 11701
Cusp forms 18920 7699 11221
Eisenstein series 560 80 480

Trace form

\( 7699 q + 6 q^{2} - 161 q^{3} - 72 q^{4} + 1788 q^{5} - 3412 q^{6} - 10274 q^{7} + 21960 q^{8} + 17967 q^{9} + O(q^{10}) \) \( 7699 q + 6 q^{2} - 161 q^{3} - 72 q^{4} + 1788 q^{5} - 3412 q^{6} - 10274 q^{7} + 21960 q^{8} + 17967 q^{9} - 48960 q^{10} - 47232 q^{11} + 60258 q^{12} + 308478 q^{13} + 328488 q^{14} - 184546 q^{15} - 362708 q^{16} + 1410780 q^{17} - 577564 q^{18} - 1281858 q^{19} + 562380 q^{20} - 1065890 q^{21} + 524468 q^{22} + 1347720 q^{23} + 221616 q^{24} - 1081916 q^{25} - 880932 q^{26} - 1290161 q^{27} + 5021804 q^{28} + 6528312 q^{29} - 852486 q^{30} - 1917922 q^{31} + 4053816 q^{32} - 5213904 q^{33} + 7939336 q^{34} + 3268884 q^{35} - 12596886 q^{36} + 13219886 q^{37} - 23214660 q^{38} - 9128178 q^{39} + 7306264 q^{40} - 10472352 q^{41} + 40693034 q^{42} + 12040766 q^{43} + 1540380 q^{44} - 23311588 q^{45} - 75434220 q^{46} - 23136000 q^{47} - 10105472 q^{48} - 11574831 q^{49} + 89505636 q^{50} + 15068552 q^{51} + 161388168 q^{52} + 16584312 q^{53} + 54545082 q^{54} - 11400512 q^{55} + 1740792 q^{56} - 104992102 q^{57} - 130829228 q^{58} - 95587200 q^{59} - 58251166 q^{60} - 125901602 q^{61} + 201573876 q^{62} + 117974716 q^{63} + 99516504 q^{64} - 131142660 q^{65} + 8741958 q^{66} + 234778846 q^{67} + 72731016 q^{68} - 71174414 q^{69} + 42951348 q^{70} - 146604960 q^{71} - 53990962 q^{72} - 191959106 q^{73} - 332570052 q^{74} + 13860578 q^{75} - 153861928 q^{76} + 8429808 q^{77} + 157444088 q^{78} + 335810486 q^{79} + 253572036 q^{80} - 475952929 q^{81} - 73849640 q^{82} - 282936480 q^{83} + 348318134 q^{84} - 674522056 q^{85} + 174856800 q^{86} + 349011790 q^{87} - 1535813044 q^{88} + 660889152 q^{89} - 499654330 q^{90} - 120000196 q^{91} - 53614104 q^{92} - 497364260 q^{93} + 3062948428 q^{94} - 496249680 q^{95} + 667014818 q^{96} - 2432645170 q^{97} - 281798130 q^{98} - 226681600 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(300))\)

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
300.9.b \(\chi_{300}(149, \cdot)\) 300.9.b.a 2 1
300.9.b.b 2
300.9.b.c 4
300.9.b.d 20
300.9.b.e 20
300.9.c \(\chi_{300}(151, \cdot)\) n/a 152 1
300.9.f \(\chi_{300}(199, \cdot)\) n/a 144 1
300.9.g \(\chi_{300}(101, \cdot)\) 300.9.g.a 1 1
300.9.g.b 1
300.9.g.c 1
300.9.g.d 2
300.9.g.e 10
300.9.g.f 10
300.9.g.g 10
300.9.g.h 16
300.9.k \(\chi_{300}(157, \cdot)\) 300.9.k.a 4 2
300.9.k.b 8
300.9.k.c 8
300.9.k.d 12
300.9.k.e 16
300.9.l \(\chi_{300}(107, \cdot)\) n/a 568 2
300.9.p \(\chi_{300}(31, \cdot)\) n/a 960 4
300.9.q \(\chi_{300}(29, \cdot)\) n/a 320 4
300.9.s \(\chi_{300}(41, \cdot)\) n/a 320 4
300.9.t \(\chi_{300}(19, \cdot)\) n/a 960 4
300.9.u \(\chi_{300}(23, \cdot)\) n/a 3808 8
300.9.v \(\chi_{300}(13, \cdot)\) n/a 320 8

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

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

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