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Properties

Label 240.5.bm
Level $240$
Weight $5$
Character orbit 240.bm
Rep. character $\chi_{240}(29,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $376$
Sturm bound $240$

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(240, [\chi])\).

Total New Old
Modular forms 392 392 0
Cusp forms 376 376 0
Eisenstein series 16 16 0

Trace form

\( 376 q - 8 q^{4} - 4 q^{6} + O(q^{10}) \) \( 376 q - 8 q^{4} - 4 q^{6} - 4 q^{10} - 4 q^{15} - 484 q^{16} - 712 q^{19} - 328 q^{21} + 748 q^{24} + 2224 q^{30} - 16 q^{31} - 9348 q^{34} + 10420 q^{36} + 5048 q^{40} - 1252 q^{45} + 8548 q^{46} + 112488 q^{49} - 328 q^{51} + 2992 q^{54} + 8184 q^{60} + 3768 q^{61} + 3040 q^{64} - 39864 q^{66} + 320 q^{69} + 12352 q^{70} - 15172 q^{75} + 67140 q^{76} - 25104 q^{79} - 8 q^{81} - 49472 q^{84} - 2504 q^{85} - 2632 q^{90} - 19216 q^{91} + 8092 q^{94} - 9656 q^{96} - 49544 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(240, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.