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Properties

Label 240.3.bm
Level $240$
Weight $3$
Character orbit 240.bm
Rep. character $\chi_{240}(29,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $184$
Newform subspaces $2$
Sturm bound $144$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.bm (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

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

Trace form

\( 184 q - 8 q^{4} - 4 q^{6} + O(q^{10}) \) \( 184 q - 8 q^{4} - 4 q^{6} - 4 q^{10} - 4 q^{15} - 36 q^{16} + 24 q^{19} - 40 q^{21} - 20 q^{24} - 128 q^{30} - 16 q^{31} + 76 q^{34} - 140 q^{36} - 136 q^{40} - 52 q^{45} - 172 q^{46} + 936 q^{49} - 40 q^{51} - 32 q^{54} - 72 q^{60} - 40 q^{61} - 32 q^{64} + 72 q^{66} + 32 q^{69} - 416 q^{70} + 92 q^{75} - 124 q^{76} - 272 q^{79} - 8 q^{81} - 128 q^{84} - 104 q^{85} + 152 q^{90} - 400 q^{91} - 84 q^{94} + 520 q^{96} - 200 q^{99} + O(q^{100}) \)

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.bm.a 240.bm 240.am $8$ $6.540$ 8.0.3317760000.4 \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}-3\beta _{3}q^{3}+(4\beta _{4}+\beta _{6})q^{4}+\cdots\)
240.3.bm.b 240.bm 240.am $176$ $6.540$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$