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Properties

Label 450.6.h
Level $450$
Weight $6$
Character orbit 450.h
Rep. character $\chi_{450}(91,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $252$
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.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1832 252 1580
Cusp forms 1768 252 1516
Eisenstein series 64 0 64

Trace form

\( 252 q + 4 q^{2} - 1008 q^{4} + 199 q^{5} + 160 q^{7} + 64 q^{8} + O(q^{10}) \) \( 252 q + 4 q^{2} - 1008 q^{4} + 199 q^{5} + 160 q^{7} + 64 q^{8} - 404 q^{10} - 232 q^{11} + 1186 q^{13} + 784 q^{14} - 16128 q^{16} - 1144 q^{17} + 4546 q^{19} - 576 q^{20} - 1408 q^{22} + 4350 q^{23} + 21097 q^{25} - 21000 q^{26} + 5600 q^{28} - 4128 q^{29} - 1098 q^{31} - 4096 q^{32} - 12340 q^{34} + 15894 q^{35} + 12097 q^{37} - 15376 q^{38} - 6464 q^{40} + 10700 q^{41} - 31492 q^{43} + 8928 q^{44} + 11744 q^{46} - 310 q^{47} + 636868 q^{49} - 10076 q^{50} + 18976 q^{52} - 107811 q^{53} + 103718 q^{55} + 12544 q^{56} + 72 q^{58} - 111600 q^{59} - 55460 q^{61} + 127472 q^{62} - 258048 q^{64} + 280683 q^{65} + 35282 q^{67} + 36576 q^{68} - 27392 q^{70} - 155802 q^{71} - 86562 q^{73} - 160424 q^{74} - 9984 q^{76} - 365160 q^{77} + 8760 q^{79} - 23296 q^{80} + 272024 q^{82} + 569422 q^{83} + 195863 q^{85} + 174808 q^{86} - 3968 q^{88} + 689 q^{89} - 222116 q^{91} - 56160 q^{92} - 220512 q^{94} + 253044 q^{95} - 82426 q^{97} + 218756 q^{98} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)