Properties

Label 368.2.c
Level $368$
Weight $2$
Character orbit 368.c
Rep. character $\chi_{368}(367,\cdot)$
Character field $\Q$
Dimension $12$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q\)
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 54 12 42
Cusp forms 42 12 30
Eisenstein series 12 0 12

Trace form

\( 12q - 12q^{9} + O(q^{10}) \) \( 12q - 12q^{9} - 12q^{25} - 24q^{29} + 24q^{41} + 36q^{49} - 24q^{69} + 72q^{77} - 60q^{81} + 24q^{85} + 24q^{93} + O(q^{100}) \)

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.c.a \(4\) \(2.938\) \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}-2q^{9}+3\beta _{1}q^{11}+\cdots\)
368.2.c.b \(8\) \(2.938\) 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+\beta _{6}q^{7}+\beta _{7}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 3}\)