Properties

Label 756.2.bp
Level 756
Weight 2
Character orbit bp
Rep. character \(\chi_{756}(193,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 144
Newform subspaces 1
Sturm bound 288
Trace bound 0

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Defining parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.bp (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).

Total New Old
Modular forms 900 144 756
Cusp forms 828 144 684
Eisenstein series 72 0 72

Trace form

\( 144q - 12q^{9} + O(q^{10}) \) \( 144q - 12q^{9} - 12q^{11} - 12q^{15} - 24q^{17} - 3q^{21} + 15q^{23} + 6q^{29} + 18q^{33} + 18q^{35} + 18q^{39} - 12q^{41} + 6q^{45} + 18q^{47} + 36q^{49} + 18q^{51} + 15q^{53} + 3q^{57} + 30q^{59} + 18q^{61} + 3q^{63} + 9q^{65} + 30q^{69} - 12q^{71} - 36q^{73} + 102q^{75} + 69q^{77} + 18q^{79} + 12q^{81} - 36q^{85} + 78q^{87} - 72q^{89} - 18q^{91} - 60q^{93} + 42q^{95} - 72q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
756.2.bp.a \(144\) \(6.037\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(756, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database