Properties

Label 144.3.e
Level $144$
Weight $3$
Character orbit 144.e
Rep. character $\chi_{144}(17,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $72$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 60 4 56
Cusp forms 36 4 32
Eisenstein series 24 0 24

Trace form

\( 4q - 16q^{7} + O(q^{10}) \) \( 4q - 16q^{7} + 64q^{19} - 36q^{25} - 80q^{31} - 8q^{37} + 96q^{43} + 124q^{49} - 224q^{55} + 72q^{61} + 160q^{67} - 192q^{73} - 48q^{79} - 248q^{85} + 256q^{91} + 128q^{97} + O(q^{100}) \)

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.e.a \(2\) \(3.924\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-24\) \(q+5\beta q^{5}-12q^{7}+4\beta q^{11}-8q^{13}+\cdots\)
144.3.e.b \(2\) \(3.924\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(8\) \(q+\beta q^{5}+4q^{7}+4\beta q^{11}+8q^{13}+3\beta q^{17}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 2}\)