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Properties

Label 784.2.j
Level $784$
Weight $2$
Character orbit 784.j
Rep. character $\chi_{784}(195,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $152$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
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 240 168 72
Cusp forms 208 152 56
Eisenstein series 32 16 16

Trace form

\( 152 q + 4 q^{2} + 4 q^{8} + 12 q^{11} + 24 q^{16} + 20 q^{18} - 36 q^{22} - 8 q^{23} + 8 q^{29} - 44 q^{30} + 24 q^{32} - 64 q^{36} + 20 q^{37} + 8 q^{39} - 16 q^{43} - 60 q^{44} - 32 q^{46} - 56 q^{50}+ \cdots - 96 q^{99}+O(q^{100}) \) 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.j.a 784.j 112.j $56$ $6.260$ None 112.2.v.a \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
784.2.j.b 784.j 112.j $96$ $6.260$ None 784.2.j.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(784, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)