Properties

Label 900.2.bq
Level $900$
Weight $2$
Character orbit 900.bq
Rep. character $\chi_{900}(169,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $240$
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.bq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
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 1488 240 1248
Cusp forms 1392 240 1152
Eisenstein series 96 0 96

Trace form

\( 240 q + 4 q^{5} - 2 q^{9} + O(q^{10}) \) \( 240 q + 4 q^{5} - 2 q^{9} - 4 q^{11} - 35 q^{15} - 12 q^{21} - 12 q^{25} - 15 q^{27} + 12 q^{29} - 6 q^{31} - 25 q^{33} + 34 q^{35} + 8 q^{39} - 16 q^{41} - 69 q^{45} + 25 q^{47} + 120 q^{49} - 2 q^{51} + 6 q^{55} + 9 q^{59} + 5 q^{63} + 35 q^{65} + 15 q^{67} + 10 q^{69} - 38 q^{71} - 36 q^{75} - 40 q^{77} + 12 q^{79} - 18 q^{81} + 70 q^{83} + 12 q^{85} - 75 q^{87} - 58 q^{89} - 36 q^{95} - 46 q^{99} + O(q^{100}) \)

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.bq.a 900.bq 225.u $240$ $7.187$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{30}]$

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

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