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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.2.k.a \(2\) \(1.150\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(2\) \(0\) \(q+(1+i)q^{2}+2iq^{4}+(1+i)q^{5}-2iq^{7}+\cdots\)
144.2.k.b \(8\) \(1.150\) 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}+(-1-\beta _{1}-\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
144.2.k.c \(8\) \(1.150\) 8.0.629407744.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{4}-\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)

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

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