Properties

Label 288.3.u
Level $288$
Weight $3$
Character orbit 288.u
Rep. character $\chi_{288}(19,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $156$
Newform subspaces $3$
Sturm bound $144$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(288, [\chi])\).

Total New Old
Modular forms 400 164 236
Cusp forms 368 156 212
Eisenstein series 32 8 24

Trace form

\( 156q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 156q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + 36q^{10} + 4q^{11} - 4q^{13} - 12q^{14} - 4q^{19} + 84q^{20} - 80q^{22} - 60q^{23} - 4q^{25} + 104q^{26} + 56q^{28} + 4q^{29} - 16q^{32} - 48q^{34} + 100q^{35} - 4q^{37} + 116q^{38} + 40q^{40} + 4q^{41} + 92q^{43} + 84q^{44} + 28q^{46} + 8q^{47} + 4q^{50} - 428q^{52} - 156q^{53} - 260q^{55} - 160q^{56} - 176q^{58} + 132q^{59} + 60q^{61} - 168q^{62} - 136q^{64} + 8q^{65} - 36q^{67} - 488q^{68} + 8q^{70} - 252q^{71} - 4q^{73} - 524q^{74} - 308q^{76} + 228q^{77} + 504q^{79} - 640q^{80} - 404q^{82} + 484q^{83} + 96q^{85} - 240q^{86} + 112q^{88} + 4q^{89} + 188q^{91} + 168q^{92} + 760q^{94} - 8q^{97} + 56q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
288.3.u.a \(28\) \(7.847\) None \(4\) \(0\) \(4\) \(-4\)
288.3.u.b \(64\) \(7.847\) None \(0\) \(0\) \(0\) \(0\)
288.3.u.c \(64\) \(7.847\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)