Properties

Label 2002.2.c
Level 2002
Weight 2
Character orbit c
Rep. character \(\chi_{2002}(1847,\cdot)\)
Character field \(\Q\)
Dimension 96
Newform subspaces 2
Sturm bound 672
Trace bound 7

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Defining parameters

Level: \( N \) = \( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2002.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(672\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2002, [\chi])\).

Total New Old
Modular forms 344 96 248
Cusp forms 328 96 232
Eisenstein series 16 0 16

Trace form

\( 96q - 96q^{4} - 96q^{9} + O(q^{10}) \) \( 96q - 96q^{4} - 96q^{9} - 8q^{11} - 4q^{14} + 16q^{15} + 96q^{16} + 4q^{22} - 64q^{23} - 112q^{25} + 96q^{36} - 32q^{37} + 32q^{42} + 8q^{44} - 76q^{49} + 8q^{53} + 4q^{56} + 48q^{58} - 16q^{60} - 96q^{64} - 16q^{67} - 40q^{70} - 24q^{77} + 32q^{81} - 4q^{88} + 16q^{91} + 64q^{92} - 96q^{93} + 184q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2002, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2002.2.c.a \(48\) \(15.986\) None \(0\) \(0\) \(0\) \(-8\)
2002.2.c.b \(48\) \(15.986\) None \(0\) \(0\) \(0\) \(8\)

Decomposition of \(S_{2}^{\mathrm{old}}(2002, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2002, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1001, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database