# Properties

 Label 3006.2 Level 3006 Weight 2 Dimension 66230 Nonzero newspaces 8 Sturm bound 1003968 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$3006 = 2 \cdot 3^{2} \cdot 167$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Sturm bound: $$1003968$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3006))$$.

Total New Old
Modular forms 253648 66230 187418
Cusp forms 248337 66230 182107
Eisenstein series 5311 0 5311

## Trace form

 $$66230q + 2q^{2} + 6q^{3} + 2q^{4} - 6q^{6} + 4q^{7} - 4q^{8} - 6q^{9} + O(q^{10})$$ $$66230q + 2q^{2} + 6q^{3} + 2q^{4} - 6q^{6} + 4q^{7} - 4q^{8} - 6q^{9} - 6q^{11} + 4q^{13} + 4q^{14} + 2q^{16} + 12q^{17} + 12q^{18} + 4q^{19} - 12q^{21} - 6q^{22} - 12q^{23} + 6q^{24} - 10q^{25} - 8q^{26} - 8q^{28} + 12q^{29} - 8q^{31} + 2q^{32} + 18q^{33} - 6q^{34} - 6q^{36} + 16q^{37} - 2q^{38} + 18q^{41} - 2q^{43} + 12q^{44} + 24q^{46} - 12q^{47} - 6q^{48} - 6q^{49} - 10q^{50} - 18q^{51} + 4q^{52} - 48q^{53} - 18q^{54} + 4q^{56} - 6q^{57} + 12q^{58} + 6q^{59} + 16q^{61} + 16q^{62} + 24q^{63} - 4q^{64} + 10q^{67} - 6q^{68} + 48q^{71} - 6q^{72} - 44q^{73} - 8q^{74} + 30q^{75} - 2q^{76} - 12q^{77} + 12q^{78} - 8q^{79} + 18q^{81} - 36q^{82} + 24q^{83} + 12q^{84} - 2q^{86} - 36q^{87} - 6q^{88} - 24q^{89} - 16q^{91} - 12q^{92} - 12q^{94} + 10q^{97} + 12q^{98} - 36q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3006))$$

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
3006.2.a $$\chi_{3006}(1, \cdot)$$ 3006.2.a.a 1 1
3006.2.a.b 1
3006.2.a.c 1
3006.2.a.d 1
3006.2.a.e 1
3006.2.a.f 1
3006.2.a.g 2
3006.2.a.h 2
3006.2.a.i 2
3006.2.a.j 2
3006.2.a.k 2
3006.2.a.l 2
3006.2.a.m 2
3006.2.a.n 2
3006.2.a.o 3
3006.2.a.p 3
3006.2.a.q 3
3006.2.a.r 3
3006.2.a.s 4
3006.2.a.t 5
3006.2.a.u 7
3006.2.a.v 10
3006.2.a.w 10
3006.2.d $$\chi_{3006}(3005, \cdot)$$ 3006.2.d.a 56 1
3006.2.e $$\chi_{3006}(1003, \cdot)$$ n/a 332 2
3006.2.f $$\chi_{3006}(1001, \cdot)$$ n/a 336 2
3006.2.i $$\chi_{3006}(19, \cdot)$$ n/a 5740 82
3006.2.j $$\chi_{3006}(17, \cdot)$$ n/a 4592 82
3006.2.m $$\chi_{3006}(7, \cdot)$$ n/a 27552 164
3006.2.p $$\chi_{3006}(5, \cdot)$$ n/a 27552 164

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3006))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3006)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(167))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(334))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(501))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1002))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1503))$$$$^{\oplus 2}$$