Properties

 Label 4028.2.a Level 4028 Weight 2 Character orbit a Rep. character $$\chi_{4028}(1,\cdot)$$ Character field $$\Q$$ Dimension 78 Newform subspaces 6 Sturm bound 1080 Trace bound 5

Related objects

Defining parameters

 Level: $$N$$ = $$4028 = 2^{2} \cdot 19 \cdot 53$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4028.a (trivial) Character field: $$\Q$$ Newform subspaces: $$6$$ Sturm bound: $$1080$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$, $$5$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(4028))$$.

Total New Old
Modular forms 546 78 468
Cusp forms 535 78 457
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$2$$$$19$$$$53$$FrickeDim.
$$-$$$$+$$$$+$$$$-$$$$19$$
$$-$$$$+$$$$-$$$$+$$$$19$$
$$-$$$$-$$$$+$$$$+$$$$20$$
$$-$$$$-$$$$-$$$$-$$$$20$$
Plus space$$+$$$$39$$
Minus space$$-$$$$39$$

Trace form

 $$78q + 2q^{5} - 2q^{7} + 78q^{9} + O(q^{10})$$ $$78q + 2q^{5} - 2q^{7} + 78q^{9} - 10q^{11} - 8q^{15} - 2q^{17} + 2q^{19} - 4q^{21} - 8q^{23} + 76q^{25} + 12q^{27} + 16q^{31} - 12q^{33} + 22q^{35} - 12q^{37} + 24q^{39} - 16q^{41} - 10q^{43} + 10q^{45} - 14q^{47} + 92q^{49} + 20q^{51} - 2q^{55} + 26q^{61} - 50q^{63} - 32q^{65} - 20q^{69} - 4q^{71} - 38q^{73} + 20q^{75} + 6q^{77} - 40q^{79} + 70q^{81} + 16q^{83} - 62q^{85} - 16q^{87} + 32q^{89} - 72q^{91} - 64q^{93} - 2q^{95} - 8q^{97} + 38q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(4028))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 2 19 53
4028.2.a.a $$1$$ $$32.164$$ $$\Q$$ None $$0$$ $$1$$ $$0$$ $$4$$ $$-$$ $$-$$ $$-$$ $$q+q^{3}+4q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots$$
4028.2.a.b $$1$$ $$32.164$$ $$\Q$$ None $$0$$ $$1$$ $$2$$ $$-4$$ $$-$$ $$-$$ $$+$$ $$q+q^{3}+2q^{5}-4q^{7}-2q^{9}-3q^{11}+\cdots$$
4028.2.a.c $$19$$ $$32.164$$ $$\mathbb{Q}[x]/(x^{19} - \cdots)$$ None $$0$$ $$-5$$ $$-5$$ $$-10$$ $$-$$ $$-$$ $$+$$ $$q-\beta _{1}q^{3}-\beta _{10}q^{5}+(-1+\beta _{8})q^{7}+\cdots$$
4028.2.a.d $$19$$ $$32.164$$ $$\mathbb{Q}[x]/(x^{19} - \cdots)$$ None $$0$$ $$-4$$ $$-2$$ $$-11$$ $$-$$ $$+$$ $$-$$ $$q-\beta _{1}q^{3}-\beta _{6}q^{5}+(-1+\beta _{11})q^{7}+\cdots$$
4028.2.a.e $$19$$ $$32.164$$ $$\mathbb{Q}[x]/(x^{19} - \cdots)$$ None $$0$$ $$3$$ $$3$$ $$6$$ $$-$$ $$-$$ $$-$$ $$q+\beta _{1}q^{3}+\beta _{3}q^{5}-\beta _{18}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$$
4028.2.a.f $$19$$ $$32.164$$ $$\mathbb{Q}[x]/(x^{19} - \cdots)$$ None $$0$$ $$4$$ $$4$$ $$13$$ $$-$$ $$+$$ $$+$$ $$q+\beta _{1}q^{3}+\beta _{7}q^{5}+(1+\beta _{8})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$$

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(4028))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(4028)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(19))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(38))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(53))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(76))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(106))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(212))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(1007))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(2014))$$$$^{\oplus 2}$$