Properties

Label 1815.4.m
Level $1815$
Weight $4$
Character orbit 1815.m
Rep. character $\chi_{1815}(511,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $864$
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.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 3264 864 2400
Cusp forms 3072 864 2208
Eisenstein series 192 0 192

Trace form

\( 864 q + 8 q^{2} - 904 q^{4} + 56 q^{7} - 232 q^{8} - 1944 q^{9} + O(q^{10}) \) \( 864 q + 8 q^{2} - 904 q^{4} + 56 q^{7} - 232 q^{8} - 1944 q^{9} - 160 q^{10} + 56 q^{13} + 812 q^{14} - 2744 q^{16} - 88 q^{17} - 108 q^{18} - 136 q^{19} - 80 q^{20} - 2080 q^{23} - 540 q^{24} - 5400 q^{25} - 512 q^{26} + 772 q^{28} + 1640 q^{29} + 120 q^{30} - 624 q^{31} + 3512 q^{32} + 1872 q^{34} - 520 q^{35} - 8136 q^{36} + 144 q^{37} - 2188 q^{38} + 24 q^{39} + 480 q^{40} - 1972 q^{41} - 840 q^{42} - 4416 q^{43} - 172 q^{46} - 1600 q^{47} + 1248 q^{48} - 11788 q^{49} + 200 q^{50} - 744 q^{51} + 2708 q^{52} + 4128 q^{53} + 120 q^{56} + 456 q^{57} - 500 q^{58} + 280 q^{59} - 504 q^{61} + 856 q^{62} + 504 q^{63} - 13052 q^{64} - 840 q^{65} + 448 q^{67} - 1312 q^{68} - 1296 q^{69} - 4100 q^{70} + 4344 q^{71} + 2412 q^{72} - 2120 q^{73} - 1212 q^{74} + 7776 q^{76} - 768 q^{78} - 3892 q^{79} - 640 q^{80} - 17496 q^{81} - 3852 q^{82} - 1480 q^{83} - 5328 q^{84} + 680 q^{85} - 13480 q^{86} - 9456 q^{87} - 10840 q^{89} + 360 q^{90} - 9028 q^{91} - 392 q^{92} - 5520 q^{93} - 4352 q^{94} + 1980 q^{96} - 4416 q^{97} + 3072 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)