# Properties

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

## 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

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

## 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

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