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Properties

Label 340.2.i
Level $340$
Weight $2$
Character orbit 340.i
Rep. character $\chi_{340}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $100$
Newform subspaces $3$
Sturm bound $108$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 340.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 340 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(108\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(340, [\chi])\).

Total New Old
Modular forms 116 116 0
Cusp forms 100 100 0
Eisenstein series 16 16 0

Trace form

\( 100 q - 2 q^{5} - 84 q^{9} + 2 q^{10} - 8 q^{13} + 16 q^{14} - 16 q^{16} - 14 q^{17} - 12 q^{18} + 6 q^{20} - 16 q^{21} + 8 q^{24} - 24 q^{30} + 20 q^{32} - 8 q^{33} + 4 q^{34} + 4 q^{38} - 10 q^{40} - 8 q^{41}+ \cdots + 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(340, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
340.2.i.a 340.i 340.i $2$ $2.715$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 340.2.i.a \(2\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-i+1)q^{2}-2 i q^{4}+(2 i+1)q^{5}+\cdots\)
340.2.i.b 340.i 340.i $2$ $2.715$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 340.2.i.b \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-i+1)q^{2}-2 i q^{4}+(-i+2)q^{5}+\cdots\)
340.2.i.c 340.i 340.i $96$ $2.715$ None 340.2.i.c \(-4\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$