Properties

Label 8022.2.a
Level 8022
Weight 2
Character orbit a
Rep. character \(\chi_{8022}(1,\cdot)\)
Character field \(\Q\)
Dimension 189
Newforms 27
Sturm bound 3072
Trace bound 5

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Defining parameters

Level: \( N \) = \( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8022.a (trivial)
Character field: \(\Q\)
Newforms: \( 27 \)
Sturm bound: \(3072\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8022))\).

Total New Old
Modular forms 1544 189 1355
Cusp forms 1529 189 1340
Eisenstein series 15 0 15

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

\(2\)\(3\)\(7\)\(191\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(13\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(11\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(15\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(13\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(15\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(10\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(15\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(85\)
Minus space\(-\)\(104\)

Trace form

\(189q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 189q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 189q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(189q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 189q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 189q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut q^{12} \) \(\mathstrut -\mathstrut 26q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 189q^{16} \) \(\mathstrut -\mathstrut 22q^{17} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut 187q^{25} \) \(\mathstrut -\mathstrut 10q^{26} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut +\mathstrut q^{28} \) \(\mathstrut -\mathstrut 10q^{29} \) \(\mathstrut -\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 189q^{36} \) \(\mathstrut +\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 32q^{47} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut +\mathstrut 189q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut +\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 26q^{52} \) \(\mathstrut -\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 56q^{55} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 22q^{61} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 189q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 22q^{68} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 3q^{72} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut +\mathstrut 14q^{74} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut 12q^{76} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut +\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 189q^{81} \) \(\mathstrut -\mathstrut 14q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 18q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 8q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 58q^{97} \) \(\mathstrut -\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8022))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 191
8022.2.a.a \(1\) \(64.056\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
8022.2.a.b \(1\) \(64.056\) \(\Q\) None \(-1\) \(-1\) \(3\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
8022.2.a.c \(1\) \(64.056\) \(\Q\) None \(-1\) \(1\) \(-3\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.d \(1\) \(64.056\) \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.e \(1\) \(64.056\) \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
8022.2.a.f \(1\) \(64.056\) \(\Q\) None \(1\) \(-1\) \(2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.g \(1\) \(64.056\) \(\Q\) None \(1\) \(1\) \(-2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
8022.2.a.h \(1\) \(64.056\) \(\Q\) None \(1\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
8022.2.a.i \(1\) \(64.056\) \(\Q\) None \(1\) \(1\) \(3\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
8022.2.a.j \(2\) \(64.056\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
8022.2.a.k \(2\) \(64.056\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(3\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
8022.2.a.l \(7\) \(64.056\) 7.7.118870813.1 None \(7\) \(7\) \(-8\) \(7\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
8022.2.a.m \(7\) \(64.056\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(7\) \(-3\) \(-7\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{2}+\beta _{6})q^{5}+\cdots\)
8022.2.a.n \(8\) \(64.056\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(-8\) \(9\) \(8\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{4})q^{5}+q^{6}+\cdots\)
8022.2.a.o \(8\) \(64.056\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(8\) \(2\) \(8\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
8022.2.a.p \(9\) \(64.056\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(-4\) \(9\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-\beta _{6}q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.q \(9\) \(64.056\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(6\) \(-9\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{2})q^{5}-q^{6}+\cdots\)
8022.2.a.r \(10\) \(64.056\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-10\) \(8\) \(10\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
8022.2.a.s \(11\) \(64.056\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(-11\) \(6\) \(-11\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
8022.2.a.t \(11\) \(64.056\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-11\) \(11\) \(1\) \(-11\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-q^{7}+\cdots\)
8022.2.a.u \(11\) \(64.056\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(11\) \(-11\) \(-8\) \(-11\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{4})q^{5}-q^{6}+\cdots\)
8022.2.a.v \(13\) \(64.056\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-13\) \(-13\) \(-5\) \(-13\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
8022.2.a.w \(13\) \(64.056\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-13\) \(13\) \(-2\) \(-13\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{7}+\cdots\)
8022.2.a.x \(14\) \(64.056\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(-14\) \(-10\) \(14\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
8022.2.a.y \(14\) \(64.056\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(14\) \(-4\) \(-14\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{7}+\cdots\)
8022.2.a.z \(15\) \(64.056\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-15\) \(15\) \(0\) \(15\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+q^{7}+\cdots\)
8022.2.a.ba \(16\) \(64.056\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(16\) \(11\) \(16\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(191))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(382))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(573))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1146))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1337))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2674))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\)\(^{\oplus 2}\)