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Properties

Label 900.2.br
Level $900$
Weight $2$
Character orbit 900.br
Rep. character $\chi_{900}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1408$
Newform subspaces $1$
Sturm bound $360$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 900.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 900 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(900, [\chi])\).

Total New Old
Modular forms 1472 1472 0
Cusp forms 1408 1408 0
Eisenstein series 64 64 0

Trace form

\( 1408 q - 9 q^{2} - 3 q^{4} - 24 q^{5} - 10 q^{6} - 12 q^{9} - 12 q^{10} - 6 q^{13} - 9 q^{14} - 3 q^{16} - 40 q^{18} - 33 q^{20} - 30 q^{21} - 11 q^{22} + 10 q^{24} - 8 q^{25} - 36 q^{28} - 18 q^{29} - 8 q^{30}+ \cdots - 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
900.2.br.a 900.br 900.ar $1408$ $7.187$ None 900.2.br.a \(-9\) \(0\) \(-24\) \(0\) $\mathrm{SU}(2)[C_{30}]$