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Properties

Label 150.7
Level 150
Weight 7
Dimension 830
Nonzero newspaces 6
Sturm bound 8400
Trace bound 3

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(8400\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(150))\).

Total New Old
Modular forms 3712 830 2882
Cusp forms 3488 830 2658
Eisenstein series 224 0 224

Trace form

\( 830 q + 32 q^{2} - 86 q^{3} - 64 q^{4} + 360 q^{5} + 256 q^{6} - 2780 q^{7} - 1024 q^{8} - 2254 q^{9} + O(q^{10}) \) \( 830 q + 32 q^{2} - 86 q^{3} - 64 q^{4} + 360 q^{5} + 256 q^{6} - 2780 q^{7} - 1024 q^{8} - 2254 q^{9} + 1872 q^{10} + 6496 q^{11} + 2752 q^{12} - 9764 q^{13} - 11464 q^{15} - 22528 q^{16} + 3912 q^{17} - 24592 q^{18} - 35564 q^{19} + 5632 q^{20} + 78340 q^{21} + 107520 q^{22} + 95552 q^{23} + 6144 q^{24} - 199836 q^{25} + 68096 q^{26} + 145258 q^{27} - 41600 q^{28} - 99200 q^{29} + 12480 q^{30} - 42908 q^{31} + 49152 q^{32} + 106320 q^{33} - 26928 q^{34} - 399488 q^{35} - 168768 q^{36} + 342388 q^{37} + 275968 q^{38} + 308340 q^{39} + 59904 q^{40} + 8288 q^{41} - 141824 q^{42} + 127060 q^{43} + 635780 q^{45} + 29568 q^{46} + 1337888 q^{47} - 88064 q^{48} - 2492730 q^{49} - 479632 q^{50} - 1488136 q^{51} - 119168 q^{52} - 331360 q^{53} + 1170240 q^{54} + 91056 q^{55} + 106496 q^{56} + 1785796 q^{57} + 508032 q^{58} + 2525600 q^{59} - 552448 q^{60} - 136268 q^{61} - 1075840 q^{62} + 379300 q^{63} - 65536 q^{64} - 3033716 q^{65} - 56576 q^{66} - 609836 q^{67} - 698624 q^{68} - 242496 q^{69} + 2342208 q^{70} + 3498176 q^{71} + 662528 q^{72} + 6301276 q^{73} + 952664 q^{75} - 1433216 q^{76} - 8883424 q^{77} - 295552 q^{78} - 6204476 q^{79} - 368640 q^{80} + 6832874 q^{81} + 1410048 q^{82} - 625984 q^{83} - 294528 q^{84} - 305976 q^{85} + 240384 q^{86} - 2494304 q^{87} + 2273280 q^{88} - 183700 q^{89} - 4893936 q^{90} - 2792728 q^{91} - 772096 q^{92} + 882964 q^{93} - 2734080 q^{94} + 3520736 q^{95} + 262144 q^{96} - 1779188 q^{97} + 4069408 q^{98} + 13087904 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.7.b \(\chi_{150}(149, \cdot)\) 150.7.b.a 4 1
150.7.b.b 16
150.7.b.c 16
150.7.d \(\chi_{150}(101, \cdot)\) 150.7.d.a 2 1
150.7.d.b 8
150.7.d.c 8
150.7.d.d 8
150.7.d.e 12
150.7.f \(\chi_{150}(7, \cdot)\) 150.7.f.a 4 2
150.7.f.b 4
150.7.f.c 4
150.7.f.d 4
150.7.f.e 4
150.7.f.f 4
150.7.f.g 4
150.7.f.h 8
150.7.i \(\chi_{150}(29, \cdot)\) n/a 240 4
150.7.j \(\chi_{150}(11, \cdot)\) n/a 240 4
150.7.k \(\chi_{150}(13, \cdot)\) n/a 240 8

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

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