Properties

Label 3009.2
Level 3009
Weight 2
Dimension 246971
Nonzero newspaces 20
Sturm bound 1336320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(1336320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3009))\).

Total New Old
Modular forms 337792 250387 87405
Cusp forms 330369 246971 83398
Eisenstein series 7423 3416 4007

Trace form

\( 246971 q + 9 q^{2} - 387 q^{3} - 759 q^{4} + 18 q^{5} - 381 q^{6} - 756 q^{7} + 45 q^{8} - 387 q^{9} + O(q^{10}) \) \( 246971 q + 9 q^{2} - 387 q^{3} - 759 q^{4} + 18 q^{5} - 381 q^{6} - 756 q^{7} + 45 q^{8} - 387 q^{9} - 742 q^{10} + 4 q^{11} - 417 q^{12} - 770 q^{13} + 8 q^{14} - 420 q^{15} - 831 q^{16} + 3 q^{17} - 893 q^{18} - 752 q^{19} + 14 q^{20} - 414 q^{21} - 736 q^{22} + 40 q^{23} - 425 q^{24} - 799 q^{25} - 18 q^{26} - 387 q^{27} - 804 q^{28} + 10 q^{29} - 464 q^{30} - 812 q^{31} + 29 q^{32} - 434 q^{33} - 989 q^{34} + 16 q^{35} - 433 q^{36} - 794 q^{37} + 20 q^{38} - 380 q^{39} - 766 q^{40} + 46 q^{41} - 318 q^{42} - 744 q^{43} + 124 q^{44} - 382 q^{45} - 860 q^{46} + 28 q^{47} - 533 q^{48} - 841 q^{49} - 185 q^{50} - 436 q^{51} - 1846 q^{52} - 118 q^{53} - 755 q^{54} - 1040 q^{55} - 728 q^{56} - 652 q^{57} - 1082 q^{58} - 177 q^{59} - 1446 q^{60} - 1018 q^{61} - 168 q^{62} - 800 q^{63} - 1647 q^{64} - 336 q^{65} - 848 q^{66} - 968 q^{67} - 387 q^{68} - 1222 q^{69} - 1356 q^{70} - 208 q^{71} - 885 q^{72} - 1074 q^{73} - 226 q^{74} - 611 q^{75} - 840 q^{76} - 32 q^{77} - 600 q^{78} - 796 q^{79} + 14 q^{80} - 499 q^{81} - 834 q^{82} + 28 q^{83} - 430 q^{84} - 868 q^{85} + 268 q^{86} - 300 q^{87} - 624 q^{88} + 174 q^{89} - 192 q^{90} - 636 q^{91} + 184 q^{92} - 230 q^{93} - 604 q^{94} + 232 q^{95} - 121 q^{96} - 614 q^{97} + 21 q^{98} - 274 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3009))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3009.2.a \(\chi_{3009}(1, \cdot)\) 3009.2.a.a 1 1
3009.2.a.b 2
3009.2.a.c 2
3009.2.a.d 14
3009.2.a.e 14
3009.2.a.f 16
3009.2.a.g 17
3009.2.a.h 18
3009.2.a.i 21
3009.2.a.j 24
3009.2.a.k 26
3009.2.f \(\chi_{3009}(1240, \cdot)\) n/a 172 1
3009.2.g \(\chi_{3009}(1769, \cdot)\) n/a 320 1
3009.2.h \(\chi_{3009}(3008, \cdot)\) n/a 356 1
3009.2.i \(\chi_{3009}(353, \cdot)\) n/a 712 2
3009.2.j \(\chi_{3009}(1594, \cdot)\) n/a 344 2
3009.2.n \(\chi_{3009}(178, \cdot)\) n/a 704 4
3009.2.o \(\chi_{3009}(1946, \cdot)\) n/a 1424 4
3009.2.r \(\chi_{3009}(296, \cdot)\) n/a 2784 8
3009.2.t \(\chi_{3009}(58, \cdot)\) n/a 1440 8
3009.2.u \(\chi_{3009}(154, \cdot)\) n/a 4480 28
3009.2.v \(\chi_{3009}(50, \cdot)\) n/a 9968 28
3009.2.w \(\chi_{3009}(188, \cdot)\) n/a 8960 28
3009.2.x \(\chi_{3009}(16, \cdot)\) n/a 5040 28
3009.2.be \(\chi_{3009}(4, \cdot)\) n/a 10080 56
3009.2.bf \(\chi_{3009}(38, \cdot)\) n/a 19936 56
3009.2.bh \(\chi_{3009}(2, \cdot)\) n/a 39872 112
3009.2.bi \(\chi_{3009}(19, \cdot)\) n/a 20160 112
3009.2.bk \(\chi_{3009}(10, \cdot)\) n/a 40320 224
3009.2.bm \(\chi_{3009}(5, \cdot)\) n/a 79744 224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3009))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3009)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 2}\)