Properties

Label 576.2.d
Level $576$
Weight $2$
Character orbit 576.d
Rep. character $\chi_{576}(289,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $3$
Sturm bound $192$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(576, [\chi])\).

Total New Old
Modular forms 120 10 110
Cusp forms 72 10 62
Eisenstein series 48 0 48

Trace form

\( 10q + O(q^{10}) \) \( 10q - 12q^{17} + 2q^{25} + 36q^{41} + 26q^{49} - 28q^{73} - 60q^{89} - 44q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
576.2.d.a \(2\) \(4.599\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+3iq^{11}+6q^{17}+iq^{19}+5q^{25}+\cdots\)
576.2.d.b \(4\) \(4.599\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-6q^{17}-\zeta_{12}^{3}q^{19}+\cdots\)
576.2.d.c \(4\) \(4.599\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{13}-\zeta_{12}^{3}q^{19}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)