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Properties

Label 450.6.e
Level $450$
Weight $6$
Character orbit 450.e
Rep. character $\chi_{450}(151,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $190$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 450.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(450, [\chi])\).

Total New Old
Modular forms 924 190 734
Cusp forms 876 190 686
Eisenstein series 48 0 48

Trace form

\( 190 q - 4 q^{2} + 13 q^{3} - 1520 q^{4} + 76 q^{6} - 58 q^{7} + 128 q^{8} - 557 q^{9} + O(q^{10}) \) \( 190 q - 4 q^{2} + 13 q^{3} - 1520 q^{4} + 76 q^{6} - 58 q^{7} + 128 q^{8} - 557 q^{9} + 851 q^{11} - 320 q^{12} + 362 q^{13} + 824 q^{14} - 24320 q^{16} + 1746 q^{17} + 296 q^{18} - 1018 q^{19} + 1786 q^{21} - 948 q^{22} + 8574 q^{23} - 704 q^{24} - 1424 q^{26} + 16000 q^{27} + 1856 q^{28} + 10710 q^{29} + 4976 q^{31} - 1024 q^{32} - 13461 q^{33} - 3828 q^{34} + 7792 q^{36} - 9712 q^{37} + 5284 q^{38} + 39336 q^{39} + 17999 q^{41} - 30320 q^{42} + 1469 q^{43} - 27232 q^{44} + 18960 q^{46} + 6894 q^{47} + 1792 q^{48} - 242163 q^{49} + 32833 q^{51} + 5792 q^{52} + 139056 q^{53} - 2948 q^{54} + 13184 q^{56} - 71713 q^{57} + 5016 q^{58} - 77441 q^{59} - 26176 q^{61} + 53728 q^{62} - 183988 q^{63} + 778240 q^{64} + 75560 q^{66} + 14795 q^{67} - 13968 q^{68} - 97340 q^{69} - 298104 q^{71} + 12992 q^{72} - 110842 q^{73} + 29984 q^{74} + 8144 q^{76} + 89994 q^{77} + 88936 q^{78} - 159352 q^{79} + 157543 q^{81} - 193848 q^{82} - 237288 q^{83} - 30944 q^{84} + 67052 q^{86} - 222918 q^{87} - 15168 q^{88} - 968596 q^{89} - 332072 q^{91} + 137184 q^{92} - 79120 q^{93} + 48120 q^{94} - 8192 q^{96} - 212845 q^{97} + 681576 q^{98} + 243296 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

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