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Properties

Label 240.3.ba
Level $240$
Weight $3$
Character orbit 240.ba
Rep. character $\chi_{240}(13,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.ba (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(240, [\chi])\).

Total New Old
Modular forms 200 96 104
Cusp forms 184 96 88
Eisenstein series 16 0 16

Trace form

\( 96 q - 4 q^{4} + 12 q^{8} - 288 q^{9} + O(q^{10}) \) \( 96 q - 4 q^{4} + 12 q^{8} - 288 q^{9} + 24 q^{12} - 28 q^{16} - 32 q^{19} - 84 q^{20} - 116 q^{22} - 124 q^{28} + 24 q^{30} + 140 q^{32} + 148 q^{34} - 96 q^{35} + 12 q^{36} + 160 q^{38} - 116 q^{40} - 60 q^{42} - 128 q^{43} + 48 q^{44} - 28 q^{46} - 144 q^{48} - 24 q^{50} + 96 q^{51} - 72 q^{52} + 336 q^{56} + 100 q^{58} - 128 q^{59} + 32 q^{61} + 512 q^{62} + 44 q^{64} - 72 q^{66} + 576 q^{67} - 264 q^{68} + 96 q^{69} + 4 q^{70} - 36 q^{72} - 96 q^{73} - 32 q^{74} - 192 q^{75} - 148 q^{76} - 216 q^{78} - 324 q^{80} + 864 q^{81} + 432 q^{82} - 216 q^{84} - 48 q^{86} + 668 q^{88} - 384 q^{91} + 528 q^{92} + 340 q^{94} - 768 q^{95} + 656 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.3.ba.a 240.ba 80.i $96$ $6.540$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{3}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)