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Properties

Label 900.6.i
Level $900$
Weight $6$
Character orbit 900.i
Rep. character $\chi_{900}(301,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $190$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(900, [\chi])\).

Total New Old
Modular forms 1836 190 1646
Cusp forms 1764 190 1574
Eisenstein series 72 0 72

Trace form

\( 190 q + 10 q^{3} + 29 q^{7} + 10 q^{9} + O(q^{10}) \) \( 190 q + 10 q^{3} + 29 q^{7} + 10 q^{9} + 281 q^{11} - 181 q^{13} + 3348 q^{17} - 832 q^{19} - 2495 q^{21} - 333 q^{23} + 5830 q^{27} + 5199 q^{29} - 1675 q^{31} + 11829 q^{33} + 4856 q^{37} - 29223 q^{39} - 5119 q^{41} + 1469 q^{43} - 25509 q^{47} - 223806 q^{49} + 2374 q^{51} - 36468 q^{53} + 52220 q^{57} + 38947 q^{59} + 48143 q^{61} + 7343 q^{63} + 8393 q^{67} + 42205 q^{69} + 122256 q^{71} + 15200 q^{73} - 43503 q^{77} + 12545 q^{79} + 57886 q^{81} - 25239 q^{83} + 31299 q^{87} + 531344 q^{89} + 189610 q^{91} + 67085 q^{93} - 29329 q^{97} + 157565 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)