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Properties

Label 300.8
Level 300
Weight 8
Dimension 6736
Nonzero newspaces 12
Sturm bound 38400
Trace bound 7

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Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(38400\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(300))\).

Total New Old
Modular forms 17080 6820 10260
Cusp forms 16520 6736 9784
Eisenstein series 560 84 476

Trace form

\( 6736 q - 52 q^{3} + 20 q^{4} - 62 q^{5} - 10 q^{6} + 4096 q^{7} - 4008 q^{8} - 346 q^{9} + O(q^{10}) \) \( 6736 q - 52 q^{3} + 20 q^{4} - 62 q^{5} - 10 q^{6} + 4096 q^{7} - 4008 q^{8} - 346 q^{9} - 7200 q^{10} + 3904 q^{11} + 22710 q^{12} + 4140 q^{13} - 21386 q^{15} - 193796 q^{16} - 23280 q^{17} + 99462 q^{18} + 10680 q^{19} + 113980 q^{20} + 28408 q^{21} - 233044 q^{22} - 99080 q^{23} - 639908 q^{24} - 485066 q^{25} + 426016 q^{26} + 404 q^{27} + 372172 q^{28} + 455668 q^{29} + 617194 q^{30} - 298928 q^{31} - 71080 q^{32} - 781456 q^{33} - 2083460 q^{34} + 1322164 q^{35} + 239718 q^{36} - 980002 q^{37} + 3201484 q^{38} + 3343880 q^{39} + 7556664 q^{40} + 115396 q^{41} - 7018886 q^{42} - 3609608 q^{43} - 11667740 q^{44} - 3630678 q^{45} - 2244156 q^{46} - 440960 q^{47} + 7722460 q^{48} + 7245820 q^{49} + 19849636 q^{50} + 1170076 q^{51} - 4293240 q^{52} - 478994 q^{53} - 10972648 q^{54} - 9191272 q^{55} - 9913144 q^{56} - 11657372 q^{57} - 10146888 q^{58} - 6470272 q^{59} + 13912194 q^{60} + 5163116 q^{61} + 41147364 q^{62} + 16020902 q^{63} - 26840032 q^{64} - 1266570 q^{65} + 12712478 q^{66} + 1469416 q^{67} - 16086304 q^{68} - 26800106 q^{69} - 28995132 q^{70} - 3409680 q^{71} - 36026914 q^{72} - 40562332 q^{73} + 34552998 q^{75} + 56556216 q^{76} + 30509568 q^{77} + 27024792 q^{78} + 20783336 q^{79} + 20744156 q^{80} + 82578902 q^{81} + 6315756 q^{82} + 1939880 q^{83} - 77045402 q^{84} + 86829454 q^{85} - 40903256 q^{86} + 40794750 q^{87} + 19146572 q^{88} - 163926070 q^{89} + 63153230 q^{90} - 1125616 q^{91} + 107917816 q^{92} - 20370854 q^{93} + 52454876 q^{94} - 22332080 q^{95} - 23213902 q^{96} + 186365996 q^{97} - 166380584 q^{98} + 16539552 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(300))\)

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
300.8.a \(\chi_{300}(1, \cdot)\) 300.8.a.a 1 1
300.8.a.b 1
300.8.a.c 1
300.8.a.d 1
300.8.a.e 1
300.8.a.f 1
300.8.a.g 1
300.8.a.h 1
300.8.a.i 2
300.8.a.j 2
300.8.a.k 2
300.8.a.l 2
300.8.a.m 3
300.8.a.n 3
300.8.d \(\chi_{300}(49, \cdot)\) 300.8.d.a 2 1
300.8.d.b 2
300.8.d.c 2
300.8.d.d 2
300.8.d.e 2
300.8.d.f 2
300.8.d.g 4
300.8.d.h 6
300.8.e \(\chi_{300}(251, \cdot)\) n/a 260 1
300.8.h \(\chi_{300}(299, \cdot)\) n/a 248 1
300.8.i \(\chi_{300}(257, \cdot)\) 300.8.i.a 4 2
300.8.i.b 4
300.8.i.c 16
300.8.i.d 28
300.8.i.e 32
300.8.j \(\chi_{300}(7, \cdot)\) n/a 252 2
300.8.m \(\chi_{300}(61, \cdot)\) n/a 144 4
300.8.n \(\chi_{300}(11, \cdot)\) n/a 1664 4
300.8.o \(\chi_{300}(109, \cdot)\) n/a 136 4
300.8.r \(\chi_{300}(59, \cdot)\) n/a 1664 4
300.8.w \(\chi_{300}(67, \cdot)\) n/a 1680 8
300.8.x \(\chi_{300}(17, \cdot)\) n/a 560 8

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

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