Properties

Label 900.2.bg
Level $900$
Weight $2$
Character orbit 900.bg
Rep. character $\chi_{900}(61,\cdot)$
Character field $\Q(\zeta_{15})$
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.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 240 q - 2 q^{3} - 4 q^{5} - 2 q^{9} + O(q^{10}) \) \( 240 q - 2 q^{3} - 4 q^{5} - 2 q^{9} + 4 q^{11} + 33 q^{15} - 12 q^{17} + 12 q^{21} - 12 q^{23} - 12 q^{25} + 13 q^{27} + 12 q^{29} + 6 q^{31} + 31 q^{33} + 14 q^{35} - 12 q^{37} + 8 q^{39} + 16 q^{41} + 19 q^{45} - 19 q^{47} - 120 q^{49} + 2 q^{51} + 48 q^{53} - 18 q^{55} - 54 q^{57} + 9 q^{59} + 43 q^{63} + 37 q^{65} - 9 q^{67} + 40 q^{69} - 2 q^{71} + 70 q^{75} - 40 q^{77} + 12 q^{79} - 2 q^{81} + 22 q^{83} + 12 q^{85} + 101 q^{87} + 22 q^{89} - 66 q^{93} - 16 q^{95} + 30 q^{97} - 66 q^{99} + O(q^{100}) \)

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.bg.a 900.bg 225.q $240$ $7.187$ None \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{15}]$

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

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