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Properties

Label 405.4.q
Level $405$
Weight $4$
Character orbit 405.q
Rep. character $\chi_{405}(16,\cdot)$
Character field $\Q(\zeta_{27})$
Dimension $1944$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.q (of order \(27\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 81 \)
Character field: \(\Q(\zeta_{27})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(405, [\chi])\).

Total New Old
Modular forms 2952 1944 1008
Cusp forms 2880 1944 936
Eisenstein series 72 0 72

Trace form

\( 1944 q + O(q^{10}) \) \( 1944 q - 828 q^{18} + 756 q^{23} + 2160 q^{24} + 1404 q^{27} + 1080 q^{29} - 432 q^{32} - 864 q^{33} - 1908 q^{38} - 1854 q^{41} - 7110 q^{42} - 2664 q^{44} + 1188 q^{47} + 4554 q^{48} + 846 q^{51} + 5724 q^{53} + 6678 q^{54} + 5922 q^{56} + 4428 q^{57} + 414 q^{59} - 3762 q^{62} - 3996 q^{63} + 5760 q^{65} + 11304 q^{66} + 5022 q^{68} + 378 q^{69} - 1620 q^{70} + 1440 q^{71} - 5472 q^{74} + 9720 q^{76} - 21312 q^{78} + 4212 q^{79} - 20160 q^{80} - 11520 q^{81} - 10656 q^{83} - 17136 q^{84} + 3240 q^{85} - 14400 q^{86} + 3888 q^{88} - 12690 q^{89} + 1440 q^{90} - 23940 q^{92} + 10944 q^{93} - 5508 q^{94} + 9360 q^{95} + 34470 q^{96} + 32544 q^{98} + 16992 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(405, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(405, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)