Properties

Label 144.3.o
Level $144$
Weight $3$
Character orbit 144.o
Rep. character $\chi_{144}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $3$
Sturm bound $72$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(144, [\chi])\).

Total New Old
Modular forms 108 24 84
Cusp forms 84 24 60
Eisenstein series 24 0 24

Trace form

\( 24q - 12q^{9} + O(q^{10}) \) \( 24q - 12q^{9} + 72q^{17} + 24q^{21} - 60q^{25} + 72q^{29} - 36q^{33} - 36q^{41} - 216q^{45} + 84q^{49} - 144q^{53} - 276q^{57} - 144q^{65} - 144q^{69} - 72q^{73} + 144q^{77} + 540q^{81} + 576q^{89} + 576q^{93} + 180q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.3.o.a \(8\) \(3.924\) 8.0.856615824.2 None \(0\) \(-3\) \(3\) \(3\) \(q+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
144.3.o.b \(8\) \(3.924\) 8.0.121550625.1 None \(0\) \(0\) \(-6\) \(0\) \(q+(\beta _{2}+\beta _{5})q^{3}+(-1-\beta _{1}-\beta _{7})q^{5}+\cdots\)
144.3.o.c \(8\) \(3.924\) 8.0.856615824.2 None \(0\) \(3\) \(3\) \(-3\) \(q+(-\beta _{3}+\beta _{4})q^{3}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)