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Properties

Label 360.6.d
Level $360$
Weight $6$
Character orbit 360.d
Rep. character $\chi_{360}(109,\cdot)$
Character field $\Q$
Dimension $148$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 360.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(360, [\chi])\).

Total New Old
Modular forms 368 152 216
Cusp forms 352 148 204
Eisenstein series 16 4 12

Trace form

\( 148 q + 8 q^{4} + O(q^{10}) \) \( 148 q + 8 q^{4} - 584 q^{10} - 816 q^{14} - 2324 q^{16} + 1512 q^{20} + 1556 q^{25} - 8964 q^{26} + 18688 q^{31} - 21192 q^{34} + 23420 q^{40} - 2472 q^{41} - 28500 q^{44} - 8388 q^{46} - 326540 q^{49} + 75336 q^{50} + 61272 q^{55} - 4020 q^{56} - 154852 q^{64} + 49704 q^{65} + 100092 q^{70} + 213072 q^{71} - 304380 q^{74} - 69288 q^{76} - 213664 q^{79} - 83484 q^{80} - 257964 q^{86} - 172416 q^{89} - 206316 q^{94} + 76920 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)