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Properties

Label 1521.4.h
Level $1521$
Weight $4$
Character orbit 1521.h
Rep. character $\chi_{1521}(22,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $904$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1521, [\chi])\).

Total New Old
Modular forms 1120 944 176
Cusp forms 1064 904 160
Eisenstein series 56 40 16

Trace form

\( 904 q + 2 q^{2} + q^{3} + 3538 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} + 30 q^{8} - 15 q^{9} + O(q^{10}) \) \( 904 q + 2 q^{2} + q^{3} + 3538 q^{4} + 2 q^{5} + 18 q^{6} + 11 q^{7} + 30 q^{8} - 15 q^{9} - 6 q^{10} + 18 q^{11} - 39 q^{12} + 118 q^{14} + 55 q^{15} + 13522 q^{16} + 138 q^{17} - 238 q^{18} + 32 q^{19} + 143 q^{20} + 7 q^{21} + 66 q^{22} + 223 q^{23} + 540 q^{24} - 10298 q^{25} + 346 q^{27} + 314 q^{28} - 1230 q^{29} - 388 q^{30} - 58 q^{31} + 242 q^{32} + 805 q^{33} - 6 q^{34} + 579 q^{35} + 1068 q^{36} + 86 q^{37} - 118 q^{38} + 192 q^{40} + 127 q^{41} - 229 q^{42} + 83 q^{43} - 776 q^{44} - 202 q^{45} + 18 q^{46} - 150 q^{47} - 375 q^{48} - 19449 q^{49} - 1552 q^{50} - 1120 q^{51} - 1144 q^{53} + 627 q^{54} - 123 q^{55} + 48 q^{56} + 78 q^{57} + 1254 q^{58} - 2390 q^{59} + 1083 q^{60} - 421 q^{61} + 1637 q^{62} - 2809 q^{63} + 48778 q^{64} + 2334 q^{66} - 295 q^{67} + 2112 q^{68} - 535 q^{69} - 849 q^{70} - 302 q^{71} - 270 q^{72} + 344 q^{73} + 1377 q^{74} - 106 q^{75} + 623 q^{76} + 1324 q^{77} + 668 q^{79} + 4690 q^{80} + 2273 q^{81} - 1365 q^{82} - 1392 q^{83} + 4249 q^{84} + 1188 q^{85} + 2064 q^{86} + 1089 q^{87} - 2622 q^{88} - 1808 q^{89} - 5351 q^{90} + 4046 q^{92} - 5985 q^{93} + 3021 q^{94} - 9348 q^{95} + 271 q^{96} + 1055 q^{97} + 1573 q^{98} + 5607 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1521, [\chi]) \cong \)