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Properties

Label 900.2.v
Level $900$
Weight $2$
Character orbit 900.v
Rep. character $\chi_{900}(71,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $240$
Newform subspaces $2$
Sturm bound $360$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 900.v (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(360\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 752 240 512
Cusp forms 688 240 448
Eisenstein series 64 0 64

Trace form

\( 240 q - 8 q^{10} + 24 q^{16} + 16 q^{22} - 8 q^{25} + 32 q^{28} + 32 q^{34} - 12 q^{37} + 12 q^{40} + 40 q^{46} - 224 q^{49} + 76 q^{52} + 40 q^{58} - 8 q^{61} - 48 q^{64} - 24 q^{70} + 16 q^{73} - 24 q^{76}+ \cdots + 120 q^{97}+O(q^{100}) \) 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.v.a 900.v 300.n $16$ $7.187$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-1}) \) 900.2.v.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{10}]$ \(q+\beta_{6} q^{2}+2\beta_{7} q^{4}-\beta_{8} q^{5}-2\beta_{12} q^{8}+\cdots\)
900.2.v.b 900.v 300.n $224$ $7.187$ None 900.2.v.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)