Properties

Label 756.2.bq
Level 756
Weight 2
Character orbit bq
Rep. character \(\chi_{756}(25,\cdot)\)
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.bq (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

\( 144q + 6q^{9} + O(q^{10}) \) \( 144q + 6q^{9} + 6q^{11} - 12q^{15} + 48q^{17} + 33q^{21} - 21q^{23} + 6q^{29} + 18q^{33} - 9q^{35} + 9q^{39} - 12q^{41} - 12q^{45} + 18q^{47} - 18q^{49} - 9q^{51} + 15q^{53} + 3q^{57} - 15q^{59} - 36q^{61} + 3q^{63} + 36q^{65} + 30q^{69} - 12q^{71} + 18q^{73} - 51q^{75} - 3q^{77} + 18q^{79} - 6q^{81} - 36q^{85} + 33q^{87} + 144q^{89} + 9q^{91} + 48q^{93} - 30q^{95} - 72q^{99} + O(q^{100}) \)

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.bq.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