Properties

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

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Defining parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)
Character field: \(\Q\)
Newforms: \( 11 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19 211
8018.2.a.a \(1\) \(64.024\) \(\Q\) None \(-1\) \(2\) \(1\) \(-4\) \(+\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-4q^{7}+\cdots\)
8018.2.a.b \(2\) \(64.024\) \(\Q(\sqrt{5}) \) None \(-2\) \(1\) \(0\) \(4\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\)
8018.2.a.c \(2\) \(64.024\) \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\)
8018.2.a.d \(30\) \(64.024\) None \(30\) \(-10\) \(-12\) \(-15\) \(-\) \(-\) \(+\)
8018.2.a.e \(32\) \(64.024\) None \(32\) \(-7\) \(-6\) \(-5\) \(-\) \(+\) \(-\)
8018.2.a.f \(34\) \(64.024\) None \(-34\) \(-10\) \(7\) \(-6\) \(+\) \(+\) \(+\)
8018.2.a.g \(34\) \(64.024\) None \(-34\) \(-6\) \(1\) \(-22\) \(+\) \(-\) \(-\)
8018.2.a.h \(41\) \(64.024\) None \(-41\) \(8\) \(-9\) \(7\) \(+\) \(+\) \(-\)
8018.2.a.i \(43\) \(64.024\) None \(-43\) \(0\) \(0\) \(19\) \(+\) \(-\) \(+\)
8018.2.a.j \(47\) \(64.024\) None \(47\) \(10\) \(15\) \(0\) \(-\) \(+\) \(+\)
8018.2.a.k \(49\) \(64.024\) None \(49\) \(13\) \(17\) \(22\) \(-\) \(-\) \(-\)

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

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