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Properties

Label 945.2.be
Level $945$
Weight $2$
Character orbit 945.be
Rep. character $\chi_{945}(206,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $3$
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.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
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 64 248
Cusp forms 264 64 200
Eisenstein series 48 0 48

Trace form

\( 64 q + 32 q^{4} + 2 q^{7} + O(q^{10}) \) \( 64 q + 32 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 32 q^{16} + 64 q^{25} + 24 q^{26} - 8 q^{28} - 18 q^{29} + 24 q^{31} - 2 q^{37} + 120 q^{38} - 6 q^{41} - 8 q^{43} + 42 q^{44} + 6 q^{46} + 36 q^{47} + 10 q^{49} - 48 q^{53} - 102 q^{56} - 30 q^{59} - 60 q^{61} - 64 q^{64} - 6 q^{65} + 14 q^{67} + 60 q^{68} + 6 q^{70} + 54 q^{77} - 4 q^{79} - 60 q^{83} - 6 q^{85} + 42 q^{89} - 6 q^{91} - 12 q^{92} - 6 q^{97} + 54 q^{98} + O(q^{100}) \)

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.be.a 945.be 63.s $2$ $7.546$ \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
945.2.be.b 945.be 63.s $30$ $7.546$ None \(-3\) \(0\) \(-30\) \(6\) $\mathrm{SU}(2)[C_{6}]$
945.2.be.c 945.be 63.s $32$ $7.546$ None \(0\) \(0\) \(32\) \(1\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)