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Properties

Label 945.2.bo
Level $945$
Weight $2$
Character orbit 945.bo
Rep. character $\chi_{945}(289,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $2$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 945.bo (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

Total New Old
Modular forms 312 104 208
Cusp forms 264 88 176
Eisenstein series 48 16 32

Trace form

\( 88 q + 42 q^{4} + 2 q^{5} + O(q^{10}) \) \( 88 q + 42 q^{4} + 2 q^{5} + 2 q^{10} + 8 q^{14} - 34 q^{16} - 4 q^{19} + 12 q^{20} - 2 q^{25} + 32 q^{26} + 14 q^{29} + 2 q^{31} - 8 q^{34} - 24 q^{35} + 16 q^{40} + 34 q^{41} + 16 q^{44} + 10 q^{46} - 14 q^{49} - 34 q^{50} - 30 q^{55} - 18 q^{56} - 50 q^{59} + 8 q^{61} - 56 q^{64} + 8 q^{65} - 24 q^{70} - 12 q^{71} + 76 q^{74} + 12 q^{76} - 4 q^{79} + 7 q^{80} - 7 q^{85} + 88 q^{86} - 40 q^{89} - 36 q^{91} - 2 q^{94} + 37 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
945.2.bo.a 945.bo 315.ao $4$ $7.546$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}^{2}q^{4}+(-1+2\zeta_{12}^{3})q^{5}+\cdots\)
945.2.bo.b 945.bo 315.ao $84$ $7.546$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)