# Properties

 Label 3004.2 Level 3004 Weight 2 Dimension 163750 Nonzero newspaces 16 Sturm bound 1128000 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$3004 = 2^{2} \cdot 751$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$16$$ Sturm bound: $$1128000$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3004))$$.

Total New Old
Modular forms 283875 165250 118625
Cusp forms 280126 163750 116376
Eisenstein series 3749 1500 2249

## Trace form

 $$163750q - 375q^{2} - 375q^{4} - 750q^{5} - 375q^{6} - 375q^{8} - 750q^{9} + O(q^{10})$$ $$163750q - 375q^{2} - 375q^{4} - 750q^{5} - 375q^{6} - 375q^{8} - 750q^{9} - 375q^{10} - 375q^{12} - 750q^{13} - 375q^{14} - 375q^{16} - 750q^{17} - 375q^{18} - 375q^{20} - 750q^{21} - 375q^{22} - 375q^{24} - 750q^{25} - 375q^{26} - 375q^{28} - 750q^{29} - 375q^{30} - 375q^{32} - 750q^{33} - 375q^{34} - 375q^{36} - 750q^{37} - 375q^{38} - 375q^{40} - 750q^{41} - 375q^{42} - 375q^{44} - 750q^{45} - 375q^{46} - 375q^{48} - 750q^{49} - 375q^{50} - 375q^{52} - 750q^{53} - 375q^{54} - 375q^{56} - 750q^{57} - 375q^{58} - 375q^{60} - 750q^{61} - 375q^{62} - 375q^{64} - 750q^{65} - 375q^{66} - 375q^{68} - 750q^{69} - 375q^{70} - 375q^{72} - 750q^{73} - 375q^{74} - 375q^{76} - 750q^{77} - 375q^{78} - 375q^{80} - 750q^{81} - 375q^{82} - 375q^{84} - 750q^{85} - 375q^{86} - 375q^{88} - 750q^{89} - 375q^{90} - 375q^{92} - 750q^{93} - 375q^{94} - 375q^{96} - 750q^{97} - 375q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3004))$$

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
3004.2.a $$\chi_{3004}(1, \cdot)$$ 3004.2.a.a 1 1
3004.2.a.b 2
3004.2.a.c 28
3004.2.a.d 31
3004.2.d $$\chi_{3004}(3003, \cdot)$$ n/a 374 1
3004.2.e $$\chi_{3004}(1429, \cdot)$$ n/a 126 2
3004.2.f $$\chi_{3004}(569, \cdot)$$ n/a 248 4
3004.2.g $$\chi_{3004}(679, \cdot)$$ n/a 748 2
3004.2.j $$\chi_{3004}(291, \cdot)$$ n/a 1496 4
3004.2.m $$\chi_{3004}(437, \cdot)$$ n/a 504 8
3004.2.n $$\chi_{3004}(53, \cdot)$$ n/a 1240 20
3004.2.q $$\chi_{3004}(583, \cdot)$$ n/a 2992 8
3004.2.r $$\chi_{3004}(195, \cdot)$$ n/a 7480 20
3004.2.u $$\chi_{3004}(61, \cdot)$$ n/a 2520 40
3004.2.v $$\chi_{3004}(45, \cdot)$$ n/a 6200 100
3004.2.y $$\chi_{3004}(11, \cdot)$$ n/a 14960 40
3004.2.ba $$\chi_{3004}(7, \cdot)$$ n/a 37400 100
3004.2.bc $$\chi_{3004}(5, \cdot)$$ n/a 12600 200
3004.2.be $$\chi_{3004}(3, \cdot)$$ n/a 74800 200

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3004))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3004)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(751))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1502))$$$$^{\oplus 2}$$