Properties

Label 8018.2.a
Level $8018$
Weight $2$
Character orbit 8018.a
Rep. character $\chi_{8018}(1,\cdot)$
Character field $\Q$
Dimension $315$
Newform subspaces $11$
Sturm bound $2120$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8018.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(2120\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8018))\).

Total New Old
Modular forms 1064 315 749
Cusp forms 1057 315 742
Eisenstein series 7 0 7

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

\(2\)\(19\)\(211\)FrickeDim
\(+\)\(+\)\(+\)$+$\(36\)
\(+\)\(+\)\(-\)$-$\(42\)
\(+\)\(-\)\(+\)$-$\(45\)
\(+\)\(-\)\(-\)$+$\(34\)
\(-\)\(+\)\(+\)$-$\(47\)
\(-\)\(+\)\(-\)$+$\(32\)
\(-\)\(-\)\(+\)$+$\(30\)
\(-\)\(-\)\(-\)$-$\(49\)
Plus space\(+\)\(132\)
Minus space\(-\)\(183\)

Trace form

\( 315 q + q^{2} + 4 q^{3} + 315 q^{4} + 14 q^{5} + 8 q^{6} + 4 q^{7} + q^{8} + 323 q^{9} + O(q^{10}) \) \( 315 q + q^{2} + 4 q^{3} + 315 q^{4} + 14 q^{5} + 8 q^{6} + 4 q^{7} + q^{8} + 323 q^{9} + 14 q^{10} + 4 q^{11} + 4 q^{12} + 6 q^{13} + 315 q^{16} - 2 q^{17} - 3 q^{18} + q^{19} + 14 q^{20} + 8 q^{21} - 4 q^{22} + 20 q^{23} + 8 q^{24} + 337 q^{25} - 2 q^{26} + 16 q^{27} + 4 q^{28} - 10 q^{29} - 8 q^{30} + 40 q^{31} + q^{32} + 8 q^{33} + 18 q^{34} - 16 q^{35} + 323 q^{36} + 38 q^{37} - q^{38} - 40 q^{39} + 14 q^{40} + 42 q^{41} - 24 q^{42} + 4 q^{43} + 4 q^{44} + 22 q^{45} + 16 q^{46} + 4 q^{47} + 4 q^{48} + 319 q^{49} - q^{50} - 32 q^{51} + 6 q^{52} - 10 q^{53} + 8 q^{54} + 56 q^{55} - 4 q^{57} + 34 q^{58} - 20 q^{59} + 26 q^{61} - 8 q^{62} + 4 q^{63} + 315 q^{64} - 20 q^{65} + 16 q^{66} + 20 q^{67} - 2 q^{68} - 16 q^{69} + 48 q^{70} + 24 q^{71} - 3 q^{72} + 38 q^{73} + 14 q^{74} - 4 q^{75} + q^{76} - 24 q^{77} - 24 q^{78} + 40 q^{79} + 14 q^{80} + 307 q^{81} + 50 q^{82} - 28 q^{83} + 8 q^{84} + 12 q^{85} - 20 q^{86} + 16 q^{87} - 4 q^{88} + 42 q^{89} - 2 q^{90} - 40 q^{91} + 20 q^{92} - 8 q^{93} + 16 q^{94} - 2 q^{95} + 8 q^{96} + 50 q^{97} + 25 q^{98} + 20 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 19 211
8018.2.a.a 8018.a 1.a $1$ $64.024$ \(\Q\) None \(-1\) \(2\) \(1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-4q^{7}+\cdots\)
8018.2.a.b 8018.a 1.a $2$ $64.024$ \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\)
8018.2.a.c 8018.a 1.a $2$ $64.024$ \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\)
8018.2.a.d 8018.a 1.a $30$ $64.024$ None \(30\) \(-10\) \(-12\) \(-15\) $-$ $-$ $+$ $\mathrm{SU}(2)$
8018.2.a.e 8018.a 1.a $32$ $64.024$ None \(32\) \(-7\) \(-6\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$
8018.2.a.f 8018.a 1.a $34$ $64.024$ None \(-34\) \(-10\) \(7\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$
8018.2.a.g 8018.a 1.a $34$ $64.024$ None \(-34\) \(-6\) \(1\) \(-22\) $+$ $-$ $-$ $\mathrm{SU}(2)$
8018.2.a.h 8018.a 1.a $41$ $64.024$ None \(-41\) \(8\) \(-9\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$
8018.2.a.i 8018.a 1.a $43$ $64.024$ None \(-43\) \(0\) \(0\) \(19\) $+$ $-$ $+$ $\mathrm{SU}(2)$
8018.2.a.j 8018.a 1.a $47$ $64.024$ None \(47\) \(10\) \(15\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$
8018.2.a.k 8018.a 1.a $49$ $64.024$ None \(49\) \(13\) \(17\) \(22\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(422))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4009))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(211))\)\(^{\oplus 4}\)