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Properties

Label 576.2.k
Level $576$
Weight $2$
Character orbit 576.k
Rep. character $\chi_{576}(145,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $18$
Newform subspaces $3$
Sturm bound $192$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 224 22 202
Cusp forms 160 18 142
Eisenstein series 64 4 60

Trace form

\( 18 q + 2 q^{5} + O(q^{10}) \) \( 18 q + 2 q^{5} - 6 q^{11} - 2 q^{13} + 4 q^{17} + 10 q^{19} + 10 q^{29} + 16 q^{31} + 20 q^{35} + 6 q^{37} + 22 q^{43} + 16 q^{47} - 10 q^{49} - 6 q^{53} + 26 q^{59} + 14 q^{61} + 12 q^{65} - 6 q^{67} - 20 q^{77} - 32 q^{79} - 42 q^{83} - 28 q^{85} - 52 q^{91} - 60 q^{95} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.2.k.a 576.k 16.e $2$ $4.599$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{5}+2iq^{7}+(1+i)q^{11}+(-1+\cdots)q^{13}+\cdots\)
576.2.k.b 576.k 16.e $8$ $4.599$ 8.0.18939904.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{4}+\beta _{6})q^{5}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
576.2.k.c 576.k 16.e $8$ $4.599$ 8.0.629407744.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)