Properties

Label 2576.2.f
Level $2576$
Weight $2$
Character orbit 2576.f
Rep. character $\chi_{2576}(321,\cdot)$
Character field $\Q$
Dimension $94$
Newform subspaces $9$
Sturm bound $768$
Trace bound $23$

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Defining parameters

Level: \( N \) \(=\) \( 2576 = 2^{4} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2576.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(768\)
Trace bound: \(23\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2576, [\chi])\).

Total New Old
Modular forms 396 98 298
Cusp forms 372 94 278
Eisenstein series 24 4 20

Trace form

\( 94 q - 94 q^{9} + O(q^{10}) \) \( 94 q - 94 q^{9} + 16 q^{23} + 82 q^{25} - 28 q^{29} - 8 q^{39} + 6 q^{49} + 8 q^{71} - 4 q^{77} + 86 q^{81} - 40 q^{85} + 24 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2576, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2576.2.f.a 2576.f 161.c $2$ $20.569$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{7}+3q^{9}-2\beta q^{11}+(-4-\beta )q^{23}+\cdots\)
2576.2.f.b 2576.f 161.c $4$ $20.569$ 4.0.2312.1 None \(0\) \(0\) \(-8\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-2q^{5}+(1-\beta _{1})q^{7}+(-2+\cdots)q^{9}+\cdots\)
2576.2.f.c 2576.f 161.c $4$ $20.569$ \(\Q(\sqrt{-2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}+4\beta _{2}q^{13}+\cdots\)
2576.2.f.d 2576.f 161.c $4$ $20.569$ \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{7}+q^{9}+\beta _{2}q^{11}+3\beta _{1}q^{13}+\cdots\)
2576.2.f.e 2576.f 161.c $4$ $20.569$ 4.0.2312.1 None \(0\) \(0\) \(8\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+2q^{5}+(-1+\beta _{1})q^{7}+(-2+\cdots)q^{9}+\cdots\)
2576.2.f.f 2576.f 161.c $12$ $20.569$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+\beta _{3}q^{5}+\beta _{7}q^{7}+(-2+\beta _{4}+\cdots)q^{9}+\cdots\)
2576.2.f.g 2576.f 161.c $16$ $20.569$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{3}+\beta _{2}q^{5}-\beta _{8}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
2576.2.f.h 2576.f 161.c $24$ $20.569$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2576.2.f.i 2576.f 161.c $24$ $20.569$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2576, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2576, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(644, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1288, [\chi])\)\(^{\oplus 2}\)