Properties

Label 4012.2.b
Level 4012
Weight 2
Character orbit b
Rep. character \(\chi_{4012}(237,\cdot)\)
Character field \(\Q\)
Dimension 86
Newform subspaces 2
Sturm bound 1080
Trace bound 1

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Defining parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(1080\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4012, [\chi])\).

Total New Old
Modular forms 546 86 460
Cusp forms 534 86 448
Eisenstein series 12 0 12

Trace form

\( 86q - 90q^{9} + O(q^{10}) \) \( 86q - 90q^{9} + 16q^{13} + 10q^{15} - 7q^{17} - 18q^{21} - 78q^{25} - 12q^{33} - 26q^{35} - 16q^{43} - 4q^{47} - 58q^{49} + 20q^{51} + 16q^{53} - 32q^{55} + 6q^{59} + 24q^{67} - 8q^{69} - 16q^{77} + 86q^{81} - 20q^{83} - 24q^{85} + 26q^{87} - 36q^{89} - 4q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4012, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4012.2.b.a \(40\) \(32.036\) None \(0\) \(0\) \(0\) \(0\)
4012.2.b.b \(46\) \(32.036\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(4012, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4012, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1003, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2006, [\chi])\)\(^{\oplus 2}\)