Properties

Label 576.2.a
Level $576$
Weight $2$
Character orbit 576.a
Rep. character $\chi_{576}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $9$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(576))\).

Total New Old
Modular forms 120 11 109
Cusp forms 73 9 64
Eisenstein series 47 2 45

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(6\)

Trace form

\( 9 q - 2 q^{5} + O(q^{10}) \) \( 9 q - 2 q^{5} + 10 q^{13} + 6 q^{17} + 7 q^{25} + 6 q^{29} + 18 q^{37} - 2 q^{41} + q^{49} + 30 q^{53} - 6 q^{61} + 12 q^{65} - 6 q^{73} - 32 q^{77} - 28 q^{85} - 18 q^{89} - 14 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(576))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
576.2.a.a 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-4q^{5}+6q^{13}+8q^{17}+11q^{25}+\cdots\)
576.2.a.b 576.a 1.a $1$ $4.599$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
576.2.a.c 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{5}-6q^{13}-2q^{17}-q^{25}-10q^{29}+\cdots\)
576.2.a.d 576.a 1.a $1$ $4.599$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
576.2.a.e 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-4q^{7}-2q^{13}-8q^{19}-5q^{25}-4q^{31}+\cdots\)
576.2.a.f 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+4q^{7}-2q^{13}+8q^{19}-5q^{25}+4q^{31}+\cdots\)
576.2.a.g 576.a 1.a $1$ $4.599$ \(\Q\) None \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
576.2.a.h 576.a 1.a $1$ $4.599$ \(\Q\) None \(0\) \(0\) \(2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots\)
576.2.a.i 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+4q^{5}+6q^{13}-8q^{17}+11q^{25}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(576))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(576)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)