Properties

Label 1002.2.a
Level $1002$
Weight $2$
Character orbit 1002.a
Rep. character $\chi_{1002}(1,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $11$
Sturm bound $336$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1002 = 2 \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1002.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1002))\).

Total New Old
Modular forms 172 29 143
Cusp forms 165 29 136
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.

\(2\)\(3\)\(167\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(11\)
Minus space\(-\)\(18\)

Trace form

\( 29q + q^{2} + q^{3} + 29q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + 29q^{9} + O(q^{10}) \) \( 29q + q^{2} + q^{3} + 29q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + 29q^{9} + 2q^{10} - 4q^{11} + q^{12} - 6q^{13} - 8q^{14} - 2q^{15} + 29q^{16} - 6q^{17} + q^{18} - 4q^{19} + 6q^{20} + 8q^{21} + 4q^{22} - 8q^{23} + q^{24} + 35q^{25} + 6q^{26} + q^{27} + 8q^{28} - 2q^{29} + 2q^{30} + 8q^{31} + q^{32} - 4q^{33} + 2q^{34} - 16q^{35} + 29q^{36} - 6q^{37} - 12q^{38} + 6q^{39} + 2q^{40} - 14q^{41} + 8q^{42} - 16q^{43} - 4q^{44} + 6q^{45} - 8q^{46} - 32q^{47} + q^{48} + 53q^{49} - q^{50} + 6q^{51} - 6q^{52} - 10q^{53} + q^{54} - 8q^{55} - 8q^{56} + 4q^{57} + 30q^{58} - 12q^{59} - 2q^{60} + 6q^{61} + 8q^{63} + 29q^{64} - 12q^{65} + 4q^{66} - 16q^{67} - 6q^{68} + 8q^{69} + 8q^{70} - 24q^{71} + q^{72} + 26q^{73} - 2q^{74} + 15q^{75} - 4q^{76} - 32q^{77} - 6q^{78} - 16q^{79} + 6q^{80} + 29q^{81} - 6q^{82} - 20q^{83} + 8q^{84} - 12q^{85} + 4q^{86} - 18q^{87} + 4q^{88} - 22q^{89} + 2q^{90} + 24q^{91} - 8q^{92} + 32q^{93} - 24q^{95} + q^{96} - 6q^{97} + 9q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 167
1002.2.a.a \(1\) \(8.001\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
1002.2.a.b \(1\) \(8.001\) \(\Q\) None \(-1\) \(-1\) \(3\) \(3\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}+3q^{7}+\cdots\)
1002.2.a.c \(1\) \(8.001\) \(\Q\) None \(-1\) \(1\) \(-1\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
1002.2.a.d \(1\) \(8.001\) \(\Q\) None \(-1\) \(1\) \(2\) \(-4\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots\)
1002.2.a.e \(1\) \(8.001\) \(\Q\) None \(1\) \(1\) \(-3\) \(-3\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-3q^{7}+\cdots\)
1002.2.a.f \(2\) \(8.001\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
1002.2.a.g \(3\) \(8.001\) 3.3.1300.1 None \(-3\) \(-3\) \(3\) \(1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
1002.2.a.h \(3\) \(8.001\) 3.3.148.1 None \(3\) \(-3\) \(-3\) \(-5\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1+\beta _{2})q^{5}-q^{6}+\cdots\)
1002.2.a.i \(4\) \(8.001\) 4.4.2777.1 None \(4\) \(-4\) \(5\) \(1\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
1002.2.a.j \(5\) \(8.001\) 5.5.11256624.1 None \(-5\) \(5\) \(-1\) \(9\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+(2+\cdots)q^{7}+\cdots\)
1002.2.a.k \(7\) \(8.001\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(7\) \(5\) \(7\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 2}\)