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Properties

Label 1815.4.be
Level $1815$
Weight $4$
Character orbit 1815.be
Rep. character $\chi_{1815}(34,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $3960$
Sturm bound $1056$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.be (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(1056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1815, [\chi])\).

Total New Old
Modular forms 7960 3960 4000
Cusp forms 7880 3960 3920
Eisenstein series 80 0 80

Trace form

\( 3960 q + 1584 q^{4} + 16 q^{5} - 24 q^{6} - 35640 q^{9} + O(q^{10}) \) \( 3960 q + 1584 q^{4} + 16 q^{5} - 24 q^{6} - 35640 q^{9} + 180 q^{10} - 532 q^{11} + 16 q^{14} - 108 q^{15} - 6192 q^{16} + 392 q^{19} + 124 q^{20} - 168 q^{21} + 288 q^{24} - 308 q^{25} - 344 q^{26} - 456 q^{30} + 768 q^{31} - 144 q^{34} + 528 q^{35} - 14256 q^{36} + 600 q^{39} - 2624 q^{40} + 504 q^{41} - 1732 q^{44} - 144 q^{45} + 976 q^{46} + 19788 q^{49} + 7060 q^{50} - 480 q^{51} + 216 q^{54} - 2568 q^{55} - 1704 q^{56} + 1912 q^{59} + 1392 q^{60} - 632 q^{61} + 23496 q^{64} + 2392 q^{65} + 1644 q^{66} - 1152 q^{69} + 1900 q^{70} - 5648 q^{71} + 8024 q^{74} + 1056 q^{75} - 21100 q^{76} + 2416 q^{79} + 648 q^{80} + 320760 q^{81} + 1944 q^{84} - 776 q^{85} - 2000 q^{86} + 1400 q^{89} - 1620 q^{90} + 1424 q^{91} - 25712 q^{94} - 6360 q^{95} - 2688 q^{96} + 4788 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1815, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)