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Properties

Label 300.7
Level 300
Weight 7
Dimension 5764
Nonzero newspaces 12
Sturm bound 33600
Trace bound 7

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Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(33600\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(300))\).

Total New Old
Modular forms 14680 5844 8836
Cusp forms 14120 5764 8356
Eisenstein series 560 80 480

Trace form

\( 5764 q - 10 q^{2} + 58 q^{3} + 136 q^{4} - 312 q^{5} + 476 q^{6} - 572 q^{7} - 2728 q^{8} - 1620 q^{9} + O(q^{10}) \) \( 5764 q - 10 q^{2} + 58 q^{3} + 136 q^{4} - 312 q^{5} + 476 q^{6} - 572 q^{7} - 2728 q^{8} - 1620 q^{9} + 4160 q^{10} + 6496 q^{11} + 5826 q^{12} + 1312 q^{13} - 40104 q^{14} - 376 q^{15} + 20140 q^{16} - 16620 q^{17} + 27908 q^{18} + 34612 q^{19} - 22420 q^{20} + 9976 q^{21} - 101932 q^{22} - 12160 q^{23} - 7776 q^{24} + 40684 q^{25} + 90156 q^{26} - 1478 q^{27} + 49292 q^{28} + 112420 q^{29} - 115926 q^{30} + 3460 q^{31} - 162440 q^{32} - 154908 q^{33} + 331144 q^{34} + 199744 q^{35} + 198042 q^{36} + 242056 q^{37} + 336124 q^{38} - 356268 q^{39} - 1336936 q^{40} - 139844 q^{41} - 668902 q^{42} + 348532 q^{43} + 729628 q^{44} + 1064432 q^{45} + 544372 q^{46} + 179360 q^{47} + 1361152 q^{48} + 1090764 q^{49} - 598364 q^{50} - 186376 q^{51} - 2893112 q^{52} - 1226444 q^{53} - 2543094 q^{54} - 2191632 q^{55} + 606776 q^{56} + 1083752 q^{57} + 4498100 q^{58} + 2525600 q^{59} + 3866354 q^{60} + 273672 q^{61} + 7812 q^{62} - 2470988 q^{63} - 4725032 q^{64} - 1951980 q^{65} - 1029210 q^{66} - 1808012 q^{67} - 3216344 q^{68} + 2134108 q^{69} + 467988 q^{70} - 404800 q^{71} + 954014 q^{72} + 4982464 q^{73} + 6971724 q^{74} - 837832 q^{75} + 2708888 q^{76} + 6591104 q^{77} - 1035880 q^{78} - 1710044 q^{79} - 2687324 q^{80} - 10299172 q^{81} - 14865992 q^{82} - 3014080 q^{83} + 769814 q^{84} - 11966936 q^{85} + 1109184 q^{86} + 4778800 q^{87} + 11243660 q^{88} - 408016 q^{89} - 1183210 q^{90} - 4762456 q^{91} - 3567832 q^{92} + 7689352 q^{93} - 13381268 q^{94} + 9420320 q^{95} + 308546 q^{96} + 16381744 q^{97} - 7353314 q^{98} - 6853600 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(300))\)

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
300.7.b \(\chi_{300}(149, \cdot)\) 300.7.b.a 2 1
300.7.b.b 2
300.7.b.c 4
300.7.b.d 12
300.7.b.e 16
300.7.c \(\chi_{300}(151, \cdot)\) n/a 114 1
300.7.f \(\chi_{300}(199, \cdot)\) n/a 108 1
300.7.g \(\chi_{300}(101, \cdot)\) 300.7.g.a 1 1
300.7.g.b 1
300.7.g.c 1
300.7.g.d 1
300.7.g.e 2
300.7.g.f 6
300.7.g.g 6
300.7.g.h 8
300.7.g.i 12
300.7.k \(\chi_{300}(157, \cdot)\) 300.7.k.a 8 2
300.7.k.b 8
300.7.k.c 8
300.7.k.d 12
300.7.l \(\chi_{300}(107, \cdot)\) n/a 424 2
300.7.p \(\chi_{300}(31, \cdot)\) n/a 720 4
300.7.q \(\chi_{300}(29, \cdot)\) n/a 240 4
300.7.s \(\chi_{300}(41, \cdot)\) n/a 240 4
300.7.t \(\chi_{300}(19, \cdot)\) n/a 720 4
300.7.u \(\chi_{300}(23, \cdot)\) n/a 2848 8
300.7.v \(\chi_{300}(13, \cdot)\) n/a 240 8

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(300)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)