Properties

Label 144.3.j
Level $144$
Weight $3$
Character orbit 144.j
Rep. character $\chi_{144}(53,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32q + O(q^{10}) \) \( 32q + 40q^{10} + 48q^{16} + 64q^{19} - 88q^{22} - 120q^{28} - 248q^{34} - 184q^{40} + 128q^{43} + 24q^{46} - 224q^{49} + 632q^{52} + 456q^{58} + 64q^{61} - 48q^{64} - 64q^{67} - 312q^{70} - 576q^{76} - 512q^{79} - 720q^{82} + 320q^{85} - 400q^{88} - 192q^{91} + 696q^{94} + O(q^{100}) \)

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.j.a \(32\) \(3.924\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{3}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)