Properties

 Label 4012.2 Level 4012 Weight 2 Dimension 288414 Nonzero newspaces 20 Sturm bound 2.00448e+06

Defining parameters

 Level: $$N$$ = $$4012 = 2^{2} \cdot 17 \cdot 59$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Sturm bound: $$2004480$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4012))$$.

Total New Old
Modular forms 505760 291830 213930
Cusp forms 496481 288414 208067
Eisenstein series 9279 3416 5863

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4012))$$

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
4012.2.a $$\chi_{4012}(1, \cdot)$$ 4012.2.a.a 1 1
4012.2.a.b 1
4012.2.a.c 1
4012.2.a.d 2
4012.2.a.e 2
4012.2.a.f 3
4012.2.a.g 12
4012.2.a.h 15
4012.2.a.i 18
4012.2.a.j 21
4012.2.b $$\chi_{4012}(237, \cdot)$$ 4012.2.b.a 40 1
4012.2.b.b 46
4012.2.e $$\chi_{4012}(3775, \cdot)$$ n/a 480 1
4012.2.f $$\chi_{4012}(4011, \cdot)$$ n/a 536 1
4012.2.j $$\chi_{4012}(1415, \cdot)$$ n/a 1072 2
4012.2.k $$\chi_{4012}(1653, \cdot)$$ n/a 172 2
4012.2.n $$\chi_{4012}(1181, \cdot)$$ n/a 352 4
4012.2.o $$\chi_{4012}(943, \cdot)$$ n/a 2144 4
4012.2.q $$\chi_{4012}(827, \cdot)$$ n/a 4176 8
4012.2.t $$\chi_{4012}(589, \cdot)$$ n/a 720 8
4012.2.u $$\chi_{4012}(137, \cdot)$$ n/a 2240 28
4012.2.x $$\chi_{4012}(67, \cdot)$$ n/a 15008 28
4012.2.y $$\chi_{4012}(103, \cdot)$$ n/a 13440 28
4012.2.bb $$\chi_{4012}(169, \cdot)$$ n/a 2520 28
4012.2.bd $$\chi_{4012}(21, \cdot)$$ n/a 5040 56
4012.2.be $$\chi_{4012}(47, \cdot)$$ n/a 30016 56
4012.2.bh $$\chi_{4012}(43, \cdot)$$ n/a 60032 112
4012.2.bi $$\chi_{4012}(9, \cdot)$$ n/a 10080 112
4012.2.bk $$\chi_{4012}(37, \cdot)$$ n/a 20160 224
4012.2.bn $$\chi_{4012}(3, \cdot)$$ n/a 120064 224

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4012))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4012)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(59))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(118))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(236))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1003))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2006))$$$$^{\oplus 2}$$