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Properties

Label 1509.2
Level 1509
Weight 2
Dimension 62749
Nonzero newspaces 4
Sturm bound 337344
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1509 = 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(337344\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1509))\).

Total New Old
Modular forms 85340 63753 21587
Cusp forms 83333 62749 20584
Eisenstein series 2007 1004 1003

Trace form

\( 62749 q - 3 q^{2} - 252 q^{3} - 509 q^{4} - 6 q^{5} - 254 q^{6} - 510 q^{7} - 15 q^{8} - 252 q^{9} + O(q^{10}) \) \( 62749 q - 3 q^{2} - 252 q^{3} - 509 q^{4} - 6 q^{5} - 254 q^{6} - 510 q^{7} - 15 q^{8} - 252 q^{9} - 520 q^{10} - 12 q^{11} - 258 q^{12} - 516 q^{13} - 24 q^{14} - 257 q^{15} - 533 q^{16} - 18 q^{17} - 254 q^{18} - 522 q^{19} - 42 q^{20} - 259 q^{21} - 538 q^{22} - 24 q^{23} - 266 q^{24} - 533 q^{25} - 42 q^{26} - 252 q^{27} - 558 q^{28} - 30 q^{29} - 269 q^{30} - 534 q^{31} - 63 q^{32} - 263 q^{33} - 556 q^{34} - 48 q^{35} - 258 q^{36} - 540 q^{37} - 60 q^{38} - 265 q^{39} - 592 q^{40} - 42 q^{41} - 275 q^{42} - 546 q^{43} - 84 q^{44} - 257 q^{45} - 574 q^{46} - 48 q^{47} - 282 q^{48} - 559 q^{49} - 93 q^{50} - 269 q^{51} - 600 q^{52} - 54 q^{53} - 254 q^{54} - 574 q^{55} - 120 q^{56} - 271 q^{57} - 592 q^{58} - 60 q^{59} - 293 q^{60} - 564 q^{61} - 96 q^{62} - 259 q^{63} - 629 q^{64} - 84 q^{65} - 287 q^{66} - 570 q^{67} - 126 q^{68} - 275 q^{69} - 646 q^{70} - 72 q^{71} - 266 q^{72} - 576 q^{73} - 114 q^{74} - 282 q^{75} - 642 q^{76} - 96 q^{77} - 293 q^{78} - 582 q^{79} - 186 q^{80} - 252 q^{81} - 628 q^{82} - 84 q^{83} - 307 q^{84} - 610 q^{85} - 132 q^{86} - 281 q^{87} - 682 q^{88} - 90 q^{89} - 269 q^{90} - 614 q^{91} - 168 q^{92} - 283 q^{93} - 646 q^{94} - 120 q^{95} - 314 q^{96} - 600 q^{97} - 171 q^{98} - 263 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1509))\)

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
1509.2.a \(\chi_{1509}(1, \cdot)\) 1509.2.a.a 1 1
1509.2.a.b 1
1509.2.a.c 2
1509.2.a.d 2
1509.2.a.e 13
1509.2.a.f 14
1509.2.a.g 24
1509.2.a.h 26
1509.2.c \(\chi_{1509}(1508, \cdot)\) n/a 166 1
1509.2.e \(\chi_{1509}(4, \cdot)\) n/a 21000 250
1509.2.g \(\chi_{1509}(5, \cdot)\) n/a 41500 250

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1509))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1509)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)\(^{\oplus 2}\)