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Properties

Label 240.2.bk
Level $240$
Weight $2$
Character orbit 240.bk
Rep. character $\chi_{240}(11,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 240.bk (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(240, [\chi])\).

Total New Old
Modular forms 104 64 40
Cusp forms 88 64 24
Eisenstein series 16 0 16

Trace form

\( 64 q + 12 q^{6} + O(q^{10}) \) \( 64 q + 12 q^{6} - 4 q^{10} + 12 q^{12} - 36 q^{16} - 20 q^{18} + 8 q^{19} - 24 q^{22} - 36 q^{24} - 24 q^{27} - 24 q^{28} - 4 q^{34} + 12 q^{36} - 48 q^{39} + 20 q^{42} + 60 q^{46} + 40 q^{48} + 64 q^{49} - 40 q^{51} + 8 q^{52} + 72 q^{54} - 104 q^{58} + 28 q^{60} - 16 q^{61} - 96 q^{64} + 24 q^{66} - 64 q^{67} - 56 q^{72} + 4 q^{76} - 40 q^{78} - 32 q^{82} - 16 q^{84} - 16 q^{85} + 8 q^{88} + 36 q^{90} + 48 q^{91} - 48 q^{93} + 28 q^{94} + 88 q^{96} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.2.bk.a 240.bk 48.k $4$ $1.916$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
240.2.bk.b 240.bk 48.k $60$ $1.916$ None \(0\) \(4\) \(0\) \(16\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)