Properties

Label 784.2.bb
Level $784$
Weight $2$
Character orbit 784.bb
Rep. character $\chi_{784}(111,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $168$
Newform subspaces $2$
Sturm bound $224$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.bb (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 2 \)
Sturm bound: \(224\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 708 168 540
Cusp forms 636 168 468
Eisenstein series 72 0 72

Trace form

\( 168 q - 28 q^{9} + O(q^{10}) \) \( 168 q - 28 q^{9} + 16 q^{21} + 52 q^{25} + 60 q^{29} - 20 q^{37} - 4 q^{49} - 24 q^{53} + 8 q^{57} - 28 q^{61} - 24 q^{65} + 168 q^{69} + 24 q^{77} - 88 q^{81} - 24 q^{85} + 40 q^{93} + O(q^{100}) \)

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.bb.a $48$ $6.260$ None \(0\) \(0\) \(0\) \(0\)
784.2.bb.b $120$ $6.260$ None \(0\) \(0\) \(0\) \(0\)

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

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