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Properties

Label 144.2.k
Level $144$
Weight $2$
Character orbit 144.k
Rep. character $\chi_{144}(37,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $18$
Newform subspaces $3$
Sturm bound $48$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 56 22 34
Cusp forms 40 18 22
Eisenstein series 16 4 12

Trace form

\( 18 q + 2 q^{2} + 2 q^{5} + 8 q^{8} + O(q^{10}) \) \( 18 q + 2 q^{2} + 2 q^{5} + 8 q^{8} + 8 q^{10} + 6 q^{11} - 2 q^{13} - 8 q^{14} - 8 q^{16} + 4 q^{17} - 10 q^{19} - 20 q^{20} - 8 q^{22} - 24 q^{26} - 16 q^{28} + 10 q^{29} - 16 q^{31} - 8 q^{32} - 36 q^{34} - 20 q^{35} + 6 q^{37} + 20 q^{38} - 16 q^{40} - 22 q^{43} + 44 q^{44} + 36 q^{46} - 16 q^{47} - 10 q^{49} + 42 q^{50} + 36 q^{52} - 6 q^{53} + 8 q^{56} + 12 q^{58} - 26 q^{59} + 14 q^{61} - 4 q^{62} + 48 q^{64} + 12 q^{65} + 6 q^{67} - 32 q^{68} + 32 q^{70} - 52 q^{74} - 36 q^{76} - 20 q^{77} + 32 q^{79} - 16 q^{80} + 42 q^{83} - 28 q^{85} + 16 q^{86} + 24 q^{88} + 52 q^{91} + 40 q^{92} + 8 q^{94} + 60 q^{95} - 4 q^{97} + 46 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.k.a 144.k 16.e $2$ $1.150$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+2iq^{4}+(1+i)q^{5}-2iq^{7}+\cdots\)
144.2.k.b 144.k 16.e $8$ $1.150$ 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}+(-1-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
144.2.k.c 144.k 16.e $8$ $1.150$ 8.0.629407744.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{4}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)