# Properties

 Label 4023.2.a Level 4023 Weight 2 Character orbit a Rep. character $$\chi_{4023}(1,\cdot)$$ Character field $$\Q$$ Dimension 198 Newform subspaces 8 Sturm bound 900 Trace bound 2

# Related objects

## Defining parameters

 Level: $$N$$ = $$4023 = 3^{3} \cdot 149$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 4023.a (trivial) Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$900$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(4023))$$.

Total New Old
Modular forms 456 198 258
Cusp forms 445 198 247
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.

$$3$$$$149$$FrickeDim.
$$+$$$$+$$$$+$$$$43$$
$$+$$$$-$$$$-$$$$57$$
$$-$$$$+$$$$-$$$$56$$
$$-$$$$-$$$$+$$$$42$$
Plus space$$+$$$$85$$
Minus space$$-$$$$113$$

## Trace form

 $$198q + 204q^{4} - 2q^{7} + O(q^{10})$$ $$198q + 204q^{4} - 2q^{7} + 4q^{10} + 6q^{13} + 216q^{16} + 14q^{19} + 20q^{22} + 214q^{25} + 16q^{28} - 8q^{31} + 14q^{37} + 12q^{40} - 12q^{43} + 16q^{46} + 216q^{49} + 60q^{52} + 28q^{55} + 40q^{58} + 38q^{61} + 240q^{64} + 42q^{67} + 84q^{70} + 18q^{73} + 48q^{76} + 34q^{79} + 52q^{82} + 72q^{85} + 64q^{88} - 6q^{91} + 16q^{94} + 14q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(4023))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 3 149
4023.2.a.a $$18$$ $$32.124$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$-1$$ $$0$$ $$1$$ $$-11$$ $$+$$ $$+$$ $$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{17}q^{5}+(-1+\cdots)q^{7}+\cdots$$
4023.2.a.b $$18$$ $$32.124$$ $$\mathbb{Q}[x]/(x^{18} - \cdots)$$ None $$1$$ $$0$$ $$-1$$ $$-11$$ $$-$$ $$-$$ $$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{17}q^{5}+(-1+\cdots)q^{7}+\cdots$$
4023.2.a.c $$24$$ $$32.124$$ None $$-7$$ $$0$$ $$-12$$ $$-1$$ $$-$$ $$-$$
4023.2.a.d $$24$$ $$32.124$$ None $$7$$ $$0$$ $$12$$ $$-1$$ $$-$$ $$+$$
4023.2.a.e $$25$$ $$32.124$$ None $$-7$$ $$0$$ $$-12$$ $$-2$$ $$+$$ $$+$$
4023.2.a.f $$25$$ $$32.124$$ None $$7$$ $$0$$ $$12$$ $$-2$$ $$+$$ $$-$$
4023.2.a.g $$32$$ $$32.124$$ None $$-1$$ $$0$$ $$1$$ $$13$$ $$+$$ $$-$$
4023.2.a.h $$32$$ $$32.124$$ None $$1$$ $$0$$ $$-1$$ $$13$$ $$-$$ $$+$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(4023))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(4023)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(27))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(149))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(447))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(1341))$$$$^{\oplus 2}$$