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Properties

Label 450.6.l
Level $450$
Weight $6$
Character orbit 450.l
Rep. character $\chi_{450}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $248$
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.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1832 248 1584
Cusp forms 1768 248 1520
Eisenstein series 64 0 64

Trace form

\( 248 q + 992 q^{4} - 284 q^{5} + O(q^{10}) \) \( 248 q + 992 q^{4} - 284 q^{5} - 408 q^{10} + 232 q^{11} + 784 q^{14} - 15872 q^{16} + 1910 q^{17} + 4546 q^{19} - 2496 q^{20} - 4720 q^{22} + 12410 q^{23} - 866 q^{25} + 17200 q^{26} + 3040 q^{28} - 7078 q^{29} + 1098 q^{31} + 5960 q^{34} - 2506 q^{35} + 12950 q^{37} + 6528 q^{40} + 10250 q^{41} + 8928 q^{44} - 11744 q^{46} + 84270 q^{47} - 563632 q^{49} - 29952 q^{50} + 22350 q^{53} + 4718 q^{55} - 12544 q^{56} - 111600 q^{59} + 74410 q^{61} - 27360 q^{62} + 253952 q^{64} + 158908 q^{65} + 145930 q^{67} + 12768 q^{70} + 284002 q^{71} - 121200 q^{73} - 156624 q^{74} + 9984 q^{76} - 194920 q^{77} + 8760 q^{79} + 1536 q^{80} + 357910 q^{83} + 657556 q^{85} - 174808 q^{86} + 56960 q^{88} + 209914 q^{89} + 222116 q^{91} - 451040 q^{92} - 220512 q^{94} - 351000 q^{95} - 288740 q^{97} - 206240 q^{98} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)