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Properties

Label 740.2.k
Level $740$
Weight $2$
Character orbit 740.k
Rep. character $\chi_{740}(179,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $220$
Newform subspaces $3$
Sturm bound $228$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 740.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 740 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(228\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(740, [\chi])\).

Total New Old
Modular forms 236 236 0
Cusp forms 220 220 0
Eisenstein series 16 16 0

Trace form

\( 220 q - 6 q^{5} + 4 q^{6} - 220 q^{9} - 4 q^{10} - 12 q^{14} - 8 q^{16} - 8 q^{20} - 36 q^{24} - 8 q^{26} - 12 q^{29} - 40 q^{34} - 72 q^{44} + 22 q^{45} - 136 q^{46} + 156 q^{49} - 20 q^{50} - 20 q^{54}+ \cdots + 16 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(740, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
740.2.k.a 740.k 740.k $2$ $5.909$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 740.2.k.a \(-2\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(i-1)q^{2}-2 i q^{4}+(-2 i-1)q^{5}+\cdots\)
740.2.k.b 740.k 740.k $2$ $5.909$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 740.2.k.a \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-i+1)q^{2}-2 i q^{4}+(i+2)q^{5}+\cdots\)
740.2.k.c 740.k 740.k $216$ $5.909$ None 740.2.k.c \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$