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Properties

Label 1512.2.t
Level $1512$
Weight $2$
Character orbit 1512.t
Rep. character $\chi_{1512}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $4$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.t (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 624 48 576
Cusp forms 528 48 480
Eisenstein series 96 0 96

Trace form

\( 48 q + 8 q^{5} + O(q^{10}) \) \( 48 q + 8 q^{5} - 8 q^{17} - 8 q^{23} + 48 q^{25} + 6 q^{29} + 6 q^{31} - 12 q^{35} - 18 q^{41} + 6 q^{43} - 6 q^{47} + 12 q^{49} - 4 q^{53} + 12 q^{55} + 36 q^{59} + 6 q^{61} - 12 q^{65} + 40 q^{71} - 4 q^{77} - 6 q^{79} + 36 q^{83} - 18 q^{89} - 6 q^{91} + 10 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1512.2.t.a 1512.t 63.g $2$ $12.073$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{5}+(-3+\zeta_{6})q^{7}+3q^{11}+(-1+\cdots)q^{13}+\cdots\)
1512.2.t.b 1512.t 63.g $2$ $12.073$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}+(1-3\zeta_{6})q^{7}-3q^{11}+(-3+\cdots)q^{13}+\cdots\)
1512.2.t.c 1512.t 63.g $22$ $12.073$ None \(0\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$
1512.2.t.d 1512.t 63.g $22$ $12.073$ None \(0\) \(0\) \(6\) \(7\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)