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Properties

Label 288.2.v
Level $288$
Weight $2$
Character orbit 288.v
Rep. character $\chi_{288}(37,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $76$
Newform subspaces $4$
Sturm bound $96$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(288, [\chi])\).

Total New Old
Modular forms 208 84 124
Cusp forms 176 76 100
Eisenstein series 32 8 24

Trace form

\( 76 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} + O(q^{10}) \) \( 76 q + 4 q^{2} - 4 q^{4} + 4 q^{5} - 4 q^{7} + 4 q^{8} - 12 q^{10} + 4 q^{11} - 4 q^{13} + 20 q^{14} - 4 q^{19} + 20 q^{20} - 24 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{26} - 24 q^{28} + 4 q^{29} + 16 q^{31} - 16 q^{32} - 16 q^{34} + 28 q^{35} - 4 q^{37} - 44 q^{38} - 56 q^{40} + 4 q^{41} + 4 q^{43} - 44 q^{44} - 36 q^{46} - 60 q^{50} - 12 q^{52} + 20 q^{53} + 28 q^{55} - 64 q^{56} - 72 q^{58} - 28 q^{59} - 36 q^{61} - 24 q^{62} + 56 q^{64} + 8 q^{65} - 12 q^{67} - 8 q^{68} + 80 q^{70} - 28 q^{71} - 4 q^{73} + 20 q^{74} + 12 q^{76} + 20 q^{77} + 64 q^{80} + 76 q^{82} - 36 q^{83} + 16 q^{85} + 88 q^{86} + 80 q^{88} + 4 q^{89} - 52 q^{91} + 120 q^{92} + 56 q^{94} - 56 q^{95} - 8 q^{97} + 104 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
288.2.v.a 288.v 32.g $4$ $2.300$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(1+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
288.2.v.b 288.v 32.g $8$ $2.300$ 8.0.18939904.2 None \(4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3}+\beta _{6})q^{4}+(\beta _{6}+\beta _{7})q^{5}+\cdots\)
288.2.v.c 288.v 32.g $32$ $2.300$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$
288.2.v.d 288.v 32.g $32$ $2.300$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

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