Properties

Label 540.2.i
Level $540$
Weight $2$
Character orbit 540.i
Rep. character $\chi_{540}(181,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $2$
Sturm bound $216$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 540.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(540, [\chi])\).

Total New Old
Modular forms 252 8 244
Cusp forms 180 8 172
Eisenstein series 72 0 72

Trace form

\( 8q - 2q^{5} - 2q^{7} + O(q^{10}) \) \( 8q - 2q^{5} - 2q^{7} - 2q^{13} + 12q^{17} + 16q^{19} - 6q^{23} - 4q^{25} + 4q^{31} + 8q^{35} + 4q^{37} + 12q^{41} - 2q^{43} + 24q^{47} - 12q^{49} + 24q^{53} - 20q^{61} - 10q^{65} - 20q^{67} - 72q^{71} + 40q^{73} + 6q^{77} + 4q^{79} - 30q^{83} + 6q^{85} + 8q^{91} - 4q^{95} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(540, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
540.2.i.a \(2\) \(4.312\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(1\) \(q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+4\zeta_{6}q^{13}+6q^{17}+\cdots\)
540.2.i.b \(6\) \(4.312\) 6.0.954288.1 None \(0\) \(0\) \(-3\) \(-3\) \(q+(-1-\beta _{2})q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(540, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(540, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)