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Properties

Label 945.2.t
Level $945$
Weight $2$
Character orbit 945.t
Rep. character $\chi_{945}(341,\cdot)$
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.t (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

\( 64 q - 64 q^{4} + 2 q^{7} + O(q^{10}) \) \( 64 q - 64 q^{4} + 2 q^{7} - 6 q^{11} + 6 q^{13} + 36 q^{14} + 64 q^{16} + 18 q^{23} - 32 q^{25} - 24 q^{26} - 8 q^{28} - 18 q^{29} - 2 q^{37} + 60 q^{38} + 6 q^{41} - 8 q^{43} - 42 q^{44} + 6 q^{46} + 72 q^{47} - 8 q^{49} - 24 q^{52} + 48 q^{53} - 78 q^{56} - 60 q^{59} - 64 q^{64} - 28 q^{67} + 30 q^{68} - 12 q^{70} - 120 q^{74} + 54 q^{77} + 8 q^{79} + 60 q^{83} - 6 q^{85} + 6 q^{86} - 42 q^{89} - 6 q^{91} - 12 q^{92} + 6 q^{97} - 54 q^{98} + O(q^{100}) \)

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.t.a 945.t 63.i $2$ $7.546$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}-q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
945.2.t.b 945.t 63.i $30$ $7.546$ None \(0\) \(0\) \(-15\) \(-3\) $\mathrm{SU}(2)[C_{6}]$
945.2.t.c 945.t 63.i $32$ $7.546$ None \(0\) \(0\) \(16\) \(1\) $\mathrm{SU}(2)[C_{6}]$

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

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