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Properties

Label 150.16
Level 150
Weight 16
Dimension 2073
Nonzero newspaces 6
Sturm bound 19200
Trace bound 1

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(19200\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(150))\).

Total New Old
Modular forms 9112 2073 7039
Cusp forms 8888 2073 6815
Eisenstein series 224 0 224

Trace form

\( 2073 q - 384 q^{2} + 3557 q^{3} - 16384 q^{4} + 840070 q^{5} - 2172544 q^{6} + 1896296 q^{7} - 6291456 q^{8} - 4782969 q^{9} + O(q^{10}) \) \( 2073 q - 384 q^{2} + 3557 q^{3} - 16384 q^{4} + 840070 q^{5} - 2172544 q^{6} + 1896296 q^{7} - 6291456 q^{8} - 4782969 q^{9} - 62835968 q^{10} + 93386764 q^{11} - 129941504 q^{12} + 1734864698 q^{13} - 550077440 q^{14} - 1333969424 q^{15} + 16911433728 q^{16} - 22436697490 q^{17} + 9520082816 q^{18} - 63682648588 q^{19} + 8962834432 q^{20} + 33711001352 q^{21} - 143352423936 q^{22} - 44186607896 q^{23} + 59624128512 q^{24} + 106994238734 q^{25} - 102688908544 q^{26} - 397014223987 q^{27} + 551020396544 q^{28} + 263014629898 q^{29} - 843069811200 q^{30} - 416657462288 q^{31} + 240518168576 q^{32} + 2530481021396 q^{33} - 5864120046080 q^{34} + 2805015486352 q^{35} - 3480914378752 q^{36} - 2323025917548 q^{37} - 1334826803712 q^{38} + 2654419607990 q^{39} + 117738307584 q^{40} + 6300105866718 q^{41} + 300477764608 q^{42} + 21888420712972 q^{43} - 14202118930432 q^{44} + 522036847830 q^{45} + 17225608107008 q^{46} - 25473581157728 q^{47} - 2128961601536 q^{48} + 7660298487201 q^{49} + 14581817872128 q^{50} + 13597435829902 q^{51} + 12289513521152 q^{52} - 120138918811308 q^{53} - 9372476469888 q^{54} + 143316782104456 q^{55} + 9588262830080 q^{56} - 194089598126868 q^{57} + 46755361865472 q^{58} - 60267086987140 q^{59} + 29724596109312 q^{60} + 24389189721874 q^{61} + 10557903058944 q^{62} - 496419777776776 q^{63} - 4398046511104 q^{64} - 320031782072626 q^{65} - 16748799809536 q^{66} + 230285453680244 q^{67} + 78820851548160 q^{68} + 74040562621976 q^{69} - 207460933650432 q^{70} - 599040159023736 q^{71} - 115854584840192 q^{72} + 1553931866096438 q^{73} + 920737163469568 q^{74} - 878244018035976 q^{75} - 103245900611584 q^{76} - 2841468157384416 q^{77} + 790052206048000 q^{78} + 2292222362626256 q^{79} + 225504573521920 q^{80} - 2631084228472017 q^{81} + 1213553772099840 q^{82} - 1352247569424532 q^{83} + 1109186594340864 q^{84} + 527151088702454 q^{85} - 1475026280816128 q^{86} - 4387038137978898 q^{87} + 986642714198016 q^{88} + 2840746615773616 q^{89} + 5472334742427904 q^{90} - 2664983663433824 q^{91} - 742311461781504 q^{92} - 7653056811110840 q^{93} - 2546345915619328 q^{94} - 5275304498294384 q^{95} + 733477334941696 q^{96} + 20926209980192390 q^{97} + 2537527093305984 q^{98} - 4146014073399012 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(150))\)

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
150.16.a \(\chi_{150}(1, \cdot)\) 150.16.a.a 1 1
150.16.a.b 1
150.16.a.c 1
150.16.a.d 1
150.16.a.e 1
150.16.a.f 1
150.16.a.g 1
150.16.a.h 1
150.16.a.i 1
150.16.a.j 1
150.16.a.k 1
150.16.a.l 2
150.16.a.m 2
150.16.a.n 2
150.16.a.o 2
150.16.a.p 2
150.16.a.q 2
150.16.a.r 2
150.16.a.s 2
150.16.a.t 3
150.16.a.u 3
150.16.a.v 3
150.16.a.w 3
150.16.a.x 4
150.16.a.y 4
150.16.c \(\chi_{150}(49, \cdot)\) 150.16.c.a 2 1
150.16.c.b 2
150.16.c.c 2
150.16.c.d 2
150.16.c.e 2
150.16.c.f 2
150.16.c.g 2
150.16.c.h 2
150.16.c.i 2
150.16.c.j 4
150.16.c.k 4
150.16.c.l 4
150.16.c.m 4
150.16.c.n 6
150.16.c.o 6
150.16.e \(\chi_{150}(107, \cdot)\) n/a 180 2
150.16.g \(\chi_{150}(31, \cdot)\) n/a 304 4
150.16.h \(\chi_{150}(19, \cdot)\) n/a 296 4
150.16.l \(\chi_{150}(17, \cdot)\) n/a 1200 8

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

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(150))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(150)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)