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Properties

Label 450.4.e
Level $450$
Weight $4$
Character orbit 450.e
Rep. character $\chi_{450}(151,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $114$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 450.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(450, [\chi])\).

Total New Old
Modular forms 564 114 450
Cusp forms 516 114 402
Eisenstein series 48 0 48

Trace form

\( 114 q + 2 q^{2} - 5 q^{3} - 228 q^{4} - 2 q^{6} + 12 q^{7} - 16 q^{8} + 115 q^{9} + O(q^{10}) \) \( 114 q + 2 q^{2} - 5 q^{3} - 228 q^{4} - 2 q^{6} + 12 q^{7} - 16 q^{8} + 115 q^{9} + 11 q^{11} - 8 q^{12} - 24 q^{13} - 100 q^{14} - 912 q^{16} - 270 q^{17} + 140 q^{18} + 210 q^{19} + 196 q^{21} - 18 q^{22} + 96 q^{23} - 56 q^{24} + 232 q^{26} - 308 q^{27} - 96 q^{28} + 108 q^{29} + 66 q^{31} + 32 q^{32} - 783 q^{33} + 90 q^{34} - 476 q^{36} + 480 q^{37} + 346 q^{38} + 882 q^{39} - 763 q^{41} + 664 q^{42} + 129 q^{43} - 88 q^{44} - 504 q^{46} - 288 q^{47} + 112 q^{48} - 2835 q^{49} + 463 q^{51} - 96 q^{52} - 1848 q^{53} + 646 q^{54} - 400 q^{56} - 2173 q^{57} - 252 q^{58} - 1133 q^{59} + 822 q^{61} + 304 q^{62} + 3338 q^{63} + 7296 q^{64} - 148 q^{66} + 363 q^{67} + 540 q^{68} - 1754 q^{69} + 7032 q^{71} + 104 q^{72} - 258 q^{73} - 16 q^{74} - 420 q^{76} + 1812 q^{77} - 2540 q^{78} + 642 q^{79} - 2825 q^{81} + 828 q^{82} + 690 q^{83} + 376 q^{84} + 446 q^{86} + 6612 q^{87} - 72 q^{88} + 5564 q^{89} + 492 q^{91} + 384 q^{92} + 1106 q^{93} - 612 q^{94} + 256 q^{96} - 2067 q^{97} - 372 q^{98} + 1058 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)