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Properties

Label 784.2.bp
Level $784$
Weight $2$
Character orbit 784.bp
Rep. character $\chi_{784}(47,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $336$
Newform subspaces $3$
Sturm bound $224$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.bp (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 3 \)
Sturm bound: \(224\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1416 336 1080
Cusp forms 1272 336 936
Eisenstein series 144 0 144

Trace form

\( 336 q + 28 q^{9} - 4 q^{21} - 16 q^{25} - 60 q^{29} + 36 q^{33} + 32 q^{37} - 36 q^{45} - 32 q^{49} - 12 q^{53} - 8 q^{57} - 8 q^{61} - 12 q^{65} - 168 q^{69} + 12 q^{73} + 48 q^{77} + 124 q^{81} + 24 q^{85}+ \cdots + 20 q^{93}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
784.2.bp.a 784.bp 196.p $108$ $6.260$ None 784.2.bp.a \(0\) \(-1\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{42}]$
784.2.bp.b 784.bp 196.p $108$ $6.260$ None 784.2.bp.a \(0\) \(1\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{42}]$
784.2.bp.c 784.bp 196.p $120$ $6.260$ None 784.2.bp.c \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{42}]$

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

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