Properties

Label 2816.2.g
Level $2816$
Weight $2$
Character orbit 2816.g
Rep. character $\chi_{2816}(1407,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $9$
Sturm bound $768$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 2816 = 2^{8} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2816.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(768\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2816, [\chi])\).

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92 q + 92 q^{9} + O(q^{10}) \) \( 92 q + 92 q^{9} - 68 q^{25} + 8 q^{33} + 60 q^{49} + 76 q^{81} + 8 q^{89} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2816, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2816.2.g.a 2816.g 88.g $4$ $22.486$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) 176.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{3}-3\beta _{1}q^{5}+8q^{9}+\beta _{2}q^{11}+\cdots\)
2816.2.g.b 2816.g 88.g $8$ $22.486$ \(\Q(\zeta_{24})\) None 44.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{4}q^{3}+\zeta_{24}q^{5}+\zeta_{24}^{6}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)
2816.2.g.c 2816.g 88.g $8$ $22.486$ 8.0.303595776.1 \(\Q(\sqrt{-11}) \) 176.2.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{7}q^{3}+(-\beta _{2}-\beta _{6})q^{5}+(1+\beta _{5}+\cdots)q^{9}+\cdots\)
2816.2.g.d 2816.g 88.g $12$ $22.486$ 12.0.\(\cdots\).1 None 352.2.e.a \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{8})q^{3}+\beta _{4}q^{5}+\beta _{11}q^{7}+\cdots\)
2816.2.g.e 2816.g 88.g $12$ $22.486$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1408.2.e.a \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+\beta _{7}q^{5}+(-1-\beta _{4})q^{7}+(1+\cdots)q^{9}+\cdots\)
2816.2.g.f 2816.g 88.g $12$ $22.486$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1408.2.e.a \(0\) \(-4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}-\beta _{7}q^{5}+(1+\beta _{4})q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
2816.2.g.g 2816.g 88.g $12$ $22.486$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1408.2.e.a \(0\) \(4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{7}q^{5}+(-1-\beta _{4})q^{7}+(1+\cdots)q^{9}+\cdots\)
2816.2.g.h 2816.g 88.g $12$ $22.486$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1408.2.e.a \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{7}q^{5}+(1+\beta _{4})q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
2816.2.g.i 2816.g 88.g $12$ $22.486$ 12.0.\(\cdots\).1 None 352.2.e.a \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{8})q^{3}+\beta _{4}q^{5}-\beta _{11}q^{7}+(1+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2816, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2816, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(704, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1408, [\chi])\)\(^{\oplus 2}\)