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Properties

Label 900.2.bt
Level $900$
Weight $2$
Character orbit 900.bt
Rep. character $\chi_{900}(77,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $480$
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.bt (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
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 2976 480 2496
Cusp forms 2784 480 2304
Eisenstein series 192 0 192

Trace form

\( 480 q + 2 q^{3} + O(q^{10}) \) \( 480 q + 2 q^{3} - 10 q^{15} + 24 q^{23} + 24 q^{25} + 26 q^{27} + 26 q^{33} - 12 q^{37} + 40 q^{39} + 90 q^{45} + 42 q^{47} - 12 q^{55} + 94 q^{57} + 30 q^{59} + 56 q^{63} + 24 q^{65} - 6 q^{67} + 70 q^{69} + 54 q^{75} + 144 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 38 q^{87} - 42 q^{93} - 60 q^{95} + 18 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
900.2.bt.a 900.bt 225.w $480$ $7.187$ None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{60}]$

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

\( S_{2}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)