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

\( 92q - 4q^{2} - 4q^{3} - 10q^{6} - 4q^{8} + O(q^{10}) \) \( 92q - 4q^{2} - 4q^{3} - 10q^{6} - 4q^{8} - 10q^{12} - 4q^{13} - 16q^{16} + 24q^{18} + 4q^{23} + 4q^{24} - 24q^{26} + 20q^{27} - 20q^{29} - 24q^{32} + 16q^{35} + 38q^{36} - 32q^{39} - 16q^{46} + 56q^{48} - 76q^{49} + 8q^{50} - 72q^{52} + 52q^{54} - 8q^{55} - 74q^{58} + 8q^{59} - 2q^{62} + 42q^{64} - 24q^{69} - 12q^{70} - 8q^{71} - 66q^{72} - 12q^{75} + 40q^{77} + 34q^{78} - 68q^{81} + 66q^{82} - 16q^{85} - 8q^{87} + 4q^{92} - 16q^{93} - 60q^{94} + 24q^{96} - 88q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
368.2.i.a \(12\) \(2.938\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{7}+\beta _{9}+\beta _{10})q^{3}+\beta _{2}q^{4}+\cdots\)
368.2.i.b \(80\) \(2.938\) None \(-4\) \(-4\) \(0\) \(0\)