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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
288.3.u.a 288.u 32.h $28$ $7.847$ None \(4\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$
288.3.u.b 288.u 32.h $64$ $7.847$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
288.3.u.c 288.u 32.h $64$ $7.847$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

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

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