Properties

Label 144.2.l
Level $144$
Weight $2$
Character orbit 144.l
Rep. character $\chi_{144}(35,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(144, [\chi])\).

Total New Old
Modular forms 56 16 40
Cusp forms 40 16 24
Eisenstein series 16 0 16

Trace form

\( 16 q + O(q^{10}) \) \( 16 q - 8 q^{10} - 16 q^{16} + 16 q^{19} - 40 q^{22} - 24 q^{28} + 24 q^{34} + 72 q^{40} - 32 q^{43} + 40 q^{46} + 16 q^{49} + 24 q^{52} - 64 q^{55} + 24 q^{58} - 32 q^{61} - 48 q^{64} - 16 q^{67} - 72 q^{70} + 80 q^{82} - 32 q^{85} + 48 q^{88} + 48 q^{91} + 72 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.2.l.a 144.l 48.k $16$ $1.150$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{11}q^{2}-\beta _{7}q^{4}+\beta _{6}q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

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