# Properties

 Label 8031.2.a Level 8031 Weight 2 Character orbit a Rep. character $$\chi_{8031}(1,\cdot)$$ Character field $$\Q$$ Dimension 447 Newform subspaces 4 Sturm bound 1785 Trace bound 1

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$8031 = 3 \cdot 2677$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 8031.a (trivial) Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$1785$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(8031))$$.

Total New Old
Modular forms 894 447 447
Cusp forms 891 447 444
Eisenstein series 3 0 3

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

$$3$$$$2677$$FrickeDim.
$$+$$$$+$$$$+$$$$102$$
$$+$$$$-$$$$-$$$$121$$
$$-$$$$+$$$$-$$$$132$$
$$-$$$$-$$$$+$$$$92$$
Plus space$$+$$$$194$$
Minus space$$-$$$$253$$

## Trace form

 $$447q - q^{2} + q^{3} + 445q^{4} + 6q^{5} - 3q^{6} - 9q^{8} + 447q^{9} + O(q^{10})$$ $$447q - q^{2} + q^{3} + 445q^{4} + 6q^{5} - 3q^{6} - 9q^{8} + 447q^{9} - 2q^{10} + 4q^{11} + 7q^{12} + 14q^{13} - 8q^{14} - 2q^{15} + 437q^{16} + 18q^{17} - q^{18} + 12q^{19} - 6q^{20} + 4q^{21} - 8q^{22} - 3q^{24} + 449q^{25} - 22q^{26} + q^{27} - 16q^{28} - 2q^{29} - 6q^{30} - 12q^{31} - 49q^{32} - 4q^{33} - 14q^{34} - 8q^{35} + 445q^{36} + 6q^{37} - 24q^{38} + 14q^{39} - 14q^{40} + 26q^{41} + 8q^{43} + 6q^{45} - 48q^{46} - q^{48} + 475q^{49} + q^{50} - 2q^{51} + 42q^{52} + 10q^{53} - 3q^{54} + 12q^{55} - 8q^{56} + 12q^{57} + 10q^{58} - 16q^{59} - 26q^{60} + 22q^{61} + 401q^{64} + 40q^{65} - 12q^{66} + 8q^{67} + 106q^{68} - 4q^{69} - 48q^{70} - 16q^{71} - 9q^{72} + 26q^{73} + 6q^{74} + 7q^{75} - 8q^{76} + 44q^{77} - 6q^{78} - 24q^{79} + 46q^{80} + 447q^{81} + 14q^{82} - 16q^{83} + 4q^{84} + 12q^{85} - 48q^{86} - 2q^{87} - 40q^{88} + 10q^{89} - 2q^{90} + 12q^{91} + 4q^{92} - 4q^{93} - 16q^{94} - 56q^{95} - 39q^{96} - 22q^{97} + 39q^{98} + 4q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(8031))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 3 2677
8031.2.a.a $$92$$ $$64.128$$ None $$-6$$ $$92$$ $$-18$$ $$-42$$ $$-$$ $$-$$
8031.2.a.b $$102$$ $$64.128$$ None $$-6$$ $$-102$$ $$-20$$ $$12$$ $$+$$ $$+$$
8031.2.a.c $$121$$ $$64.128$$ None $$7$$ $$-121$$ $$24$$ $$-14$$ $$+$$ $$-$$
8031.2.a.d $$132$$ $$64.128$$ None $$4$$ $$132$$ $$20$$ $$44$$ $$-$$ $$+$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(8031))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(8031)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(2677))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database