Properties

Label 756.2.bo
Level 756
Weight 2
Character orbit bo
Rep. character \(\chi_{756}(85,\cdot)\)
Character field \(\Q(\zeta_{9})\)
Dimension 108
Newform subspaces 2
Sturm bound 288
Trace bound 3

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Defining parameters

Level: \( N \) = \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 756.bo (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 900 108 792
Cusp forms 828 108 720
Eisenstein series 72 0 72

Trace form

\( 108q - 6q^{5} - 6q^{9} + O(q^{10}) \) \( 108q - 6q^{5} - 6q^{9} + 6q^{15} + 12q^{23} - 18q^{25} + 54q^{27} + 36q^{29} - 18q^{31} + 12q^{35} + 12q^{39} - 18q^{41} + 18q^{43} - 102q^{45} - 18q^{47} - 108q^{51} - 72q^{53} - 78q^{57} - 90q^{59} - 48q^{65} + 54q^{67} + 48q^{69} + 12q^{71} + 60q^{75} + 36q^{79} + 102q^{81} + 90q^{83} + 36q^{85} + 60q^{87} + 24q^{89} - 30q^{93} + 84q^{95} + 54q^{97} + 54q^{99} + O(q^{100}) \)

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.bo.a \(54\) \(6.037\) None \(0\) \(-3\) \(-3\) \(0\)
756.2.bo.b \(54\) \(6.037\) None \(0\) \(3\) \(-3\) \(0\)

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

\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database