↑

Properties

Label 1815.4.u
Level $1815$
Weight $4$
Character orbit 1815.u
Rep. character $\chi_{1815}(166,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $2640$
Sturm bound $1056$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.u (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 7960 2640 5320
Cusp forms 7880 2640 5240
Eisenstein series 80 0 80

Trace form

\( 2640 q - 8 q^{2} - 1016 q^{4} - 56 q^{7} + 72 q^{8} + 23760 q^{9} + O(q^{10}) \) \( 2640 q - 8 q^{2} - 1016 q^{4} - 56 q^{7} + 72 q^{8} + 23760 q^{9} - 40 q^{10} - 28 q^{11} + 40 q^{13} + 1016 q^{14} - 4024 q^{16} + 48 q^{17} - 72 q^{18} + 136 q^{19} + 108 q^{22} - 2744 q^{23} - 360 q^{24} - 6600 q^{25} + 304 q^{26} - 352 q^{28} - 240 q^{29} - 120 q^{30} + 1264 q^{31} + 48 q^{32} - 96 q^{33} - 784 q^{34} + 520 q^{35} - 9144 q^{36} - 128 q^{37} + 472 q^{38} - 24 q^{39} + 4800 q^{40} - 248 q^{41} + 936 q^{42} + 976 q^{43} - 5728 q^{44} - 208 q^{46} - 992 q^{47} - 1248 q^{48} - 10000 q^{49} - 200 q^{50} - 96 q^{51} - 4164 q^{52} + 13016 q^{53} + 60 q^{55} + 764 q^{56} - 456 q^{57} + 940 q^{58} + 1256 q^{59} - 1536 q^{61} - 8476 q^{62} - 504 q^{63} - 8872 q^{64} + 840 q^{65} - 372 q^{66} - 6504 q^{67} + 832 q^{68} + 96 q^{69} - 1080 q^{70} + 1280 q^{71} + 648 q^{72} - 6304 q^{73} + 5112 q^{74} - 9552 q^{76} + 1376 q^{77} + 15948 q^{78} - 11856 q^{79} + 213840 q^{81} - 8936 q^{82} - 560 q^{83} - 3672 q^{84} - 680 q^{85} - 6088 q^{86} - 984 q^{87} - 19436 q^{88} + 4040 q^{89} - 360 q^{90} - 728 q^{91} + 6440 q^{92} + 816 q^{93} + 16800 q^{94} + 12360 q^{96} + 960 q^{97} + 14176 q^{98} - 252 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)