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Properties

Label 368.2.i
Level $368$
Weight $2$
Character orbit 368.i
Rep. character $\chi_{368}(91,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $92$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 368.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 368 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(368, [\chi])\).

Total New Old
Modular forms 100 100 0
Cusp forms 92 92 0
Eisenstein series 8 8 0

Trace form

\( 92 q - 4 q^{2} - 4 q^{3} - 10 q^{6} - 4 q^{8} - 10 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 20 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 38 q^{36} - 32 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(368, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
368.2.i.a 368.i 368.i $12$ $2.938$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-23}) \) 368.2.i.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{1}q^{2}+(-\beta _{7}+\beta _{9}+\beta _{10})q^{3}+\beta _{2}q^{4}+\cdots\)
368.2.i.b 368.i 368.i $80$ $2.938$ None 368.2.i.b \(-4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$