Properties

Label 1001.2.b
Level 1001
Weight 2
Character orbit b
Rep. character \(\chi_{1001}(846,\cdot)\)
Character field \(\Q\)
Dimension 96
Newform subspaces 2
Sturm bound 224
Trace bound 6

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Defining parameters

Level: \( N \) = \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1001.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1001, [\chi])\).

Total New Old
Modular forms 116 96 20
Cusp forms 108 96 12
Eisenstein series 8 0 8

Trace form

\( 96q - 92q^{4} - 96q^{9} + O(q^{10}) \) \( 96q - 92q^{4} - 96q^{9} + 8q^{11} + 4q^{14} - 16q^{15} + 108q^{16} - 12q^{22} + 48q^{23} - 120q^{25} + 96q^{36} + 48q^{37} - 66q^{42} + 36q^{44} + 60q^{49} - 78q^{56} - 64q^{58} - 64q^{60} + 4q^{64} - 32q^{67} + 36q^{70} - 8q^{71} - 4q^{77} + 20q^{78} + 128q^{81} - 32q^{86} + 12q^{88} - 8q^{91} - 204q^{92} + 8q^{93} - 92q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1001, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1001.2.b.a \(48\) \(7.993\) None \(0\) \(0\) \(0\) \(4\)
1001.2.b.b \(48\) \(7.993\) None \(0\) \(0\) \(0\) \(-4\)

Decomposition of \(S_{2}^{\mathrm{old}}(1001, [\chi])\) into lower level spaces

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database