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Properties

Label 360.4.bi
Level $360$
Weight $4$
Character orbit 360.bi
Rep. character $\chi_{360}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $108$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 360.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(360, [\chi])\).

Total New Old
Modular forms 448 108 340
Cusp forms 416 108 308
Eisenstein series 32 0 32

Trace form

\( 108 q - 14 q^{9} + O(q^{10}) \) \( 108 q - 14 q^{9} - 132 q^{11} - 94 q^{15} + 188 q^{21} - 390 q^{29} + 12 q^{35} + 1040 q^{39} + 450 q^{41} - 250 q^{45} + 2448 q^{49} + 384 q^{51} - 612 q^{55} + 1848 q^{59} - 18 q^{61} + 126 q^{65} + 1562 q^{69} - 1752 q^{71} - 2026 q^{75} + 252 q^{79} - 178 q^{81} - 828 q^{85} + 3636 q^{89} - 2124 q^{95} + 680 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(360, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)