Properties

Label 784.2.f
Level $784$
Weight $2$
Character orbit 784.f
Rep. character $\chi_{784}(783,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $5$
Sturm bound $224$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(784, [\chi])\).

Total New Old
Modular forms 136 20 116
Cusp forms 88 20 68
Eisenstein series 48 0 48

Trace form

\( 20q + 20q^{9} + O(q^{10}) \) \( 20q + 20q^{9} + 4q^{25} - 24q^{29} + 8q^{37} - 24q^{53} - 40q^{57} - 72q^{65} + 92q^{81} + 24q^{85} + 88q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
784.2.f.a \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+\zeta_{6}q^{5}-2q^{9}-\zeta_{6}q^{11}-\zeta_{6}q^{15}+\cdots\)
784.2.f.b \(2\) \(6.260\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+\zeta_{6}q^{5}-2q^{9}+\zeta_{6}q^{11}+\zeta_{6}q^{15}+\cdots\)
784.2.f.c \(4\) \(6.260\) 4.0.2048.2 \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{5}-3q^{9}+(\beta _{1}+\beta _{2})q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)
784.2.f.d \(4\) \(6.260\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+4q^{9}+\beta _{3}q^{11}+\cdots\)
784.2.f.e \(8\) \(6.260\) 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(\beta _{2}-\beta _{4})q^{5}+(3-3\beta _{1})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 3}\)