Properties

Label 144.3.m
Level $144$
Weight $3$
Character orbit 144.m
Rep. character $\chi_{144}(19,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $38$
Newform subspaces $3$
Sturm bound $72$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 104 42 62
Cusp forms 88 38 50
Eisenstein series 16 4 12

Trace form

\( 38q + 2q^{2} - 8q^{4} + 2q^{5} - 4q^{7} + 8q^{8} + O(q^{10}) \) \( 38q + 2q^{2} - 8q^{4} + 2q^{5} - 4q^{7} + 8q^{8} - 4q^{10} - 14q^{11} - 2q^{13} + 32q^{14} + 24q^{16} + 4q^{17} - 34q^{19} + 4q^{20} + 84q^{22} + 68q^{23} + 4q^{26} - 64q^{28} - 14q^{29} - 168q^{32} - 4q^{34} + 4q^{35} + 46q^{37} - 208q^{38} - 224q^{40} + 14q^{43} - 108q^{44} - 60q^{46} + 178q^{49} + 190q^{50} - 212q^{52} + 82q^{53} - 260q^{55} + 392q^{56} + 280q^{58} - 78q^{59} - 34q^{61} + 420q^{62} + 112q^{64} + 20q^{65} - 162q^{67} + 336q^{68} + 344q^{70} - 252q^{71} - 256q^{74} + 148q^{76} - 12q^{77} - 784q^{80} - 16q^{82} - 158q^{83} + 108q^{85} - 796q^{86} - 440q^{88} - 4q^{91} - 328q^{92} - 744q^{94} - 4q^{97} + 430q^{98} + O(q^{100}) \)

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.m.a \(6\) \(3.924\) 6.0.399424.1 None \(2\) \(0\) \(2\) \(-4\) \(q+\beta _{3}q^{2}+(-1-\beta _{1}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
144.3.m.b \(16\) \(3.924\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(-1-\beta _{2})q^{4}+\beta _{8}q^{5}+(\beta _{11}+\cdots)q^{7}+\cdots\)
144.3.m.c \(16\) \(3.924\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

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

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