Properties

Label 1512.2.q
Level $1512$
Weight $2$
Character orbit 1512.q
Rep. character $\chi_{1512}(793,\cdot)$
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.q (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

\( 48q - 4q^{5} + O(q^{10}) \) \( 48q - 4q^{5} - 8q^{17} + 4q^{23} - 24q^{25} + 6q^{29} - 12q^{31} - 12q^{35} - 18q^{41} + 6q^{43} + 12q^{47} - 6q^{49} - 4q^{53} + 12q^{55} - 72q^{59} - 12q^{61} + 24q^{65} + 40q^{71} - 28q^{77} + 12q^{79} + 36q^{83} - 18q^{89} - 6q^{91} - 20q^{95} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1512.2.q.a \(2\) \(12.073\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-4\) \(q+(-1+\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
1512.2.q.b \(2\) \(12.073\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(4\) \(q+(1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots\)
1512.2.q.c \(22\) \(12.073\) None \(0\) \(0\) \(-3\) \(-5\)
1512.2.q.d \(22\) \(12.073\) None \(0\) \(0\) \(-1\) \(5\)

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

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)