Properties

Label 338.2.c
Level $338$
Weight $2$
Character orbit 338.c
Rep. character $\chi_{338}(191,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $26$
Newform subspaces $9$
Sturm bound $91$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 338.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
Sturm bound: \(91\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(338, [\chi])\).

Total New Old
Modular forms 118 26 92
Cusp forms 62 26 36
Eisenstein series 56 0 56

Trace form

\( 26 q + q^{2} - 13 q^{4} + 2 q^{5} + 4 q^{7} - 2 q^{8} - 17 q^{9} + O(q^{10}) \) \( 26 q + q^{2} - 13 q^{4} + 2 q^{5} + 4 q^{7} - 2 q^{8} - 17 q^{9} - q^{10} + 4 q^{11} - 12 q^{14} - 13 q^{16} + 5 q^{17} + 6 q^{18} - q^{20} + 6 q^{22} + 28 q^{25} - 12 q^{27} + 4 q^{28} + 5 q^{29} + 6 q^{30} - 8 q^{31} + q^{32} - 6 q^{34} + 6 q^{35} - 17 q^{36} + 3 q^{37} - 4 q^{38} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 4 q^{43} - 8 q^{44} + 3 q^{45} - 4 q^{46} + 16 q^{47} + 5 q^{49} - 4 q^{50} - 28 q^{51} + 6 q^{53} + 4 q^{55} + 6 q^{56} - q^{58} - 4 q^{59} + 17 q^{61} + 12 q^{62} - 12 q^{63} + 26 q^{64} - 16 q^{66} + 4 q^{67} + 5 q^{68} + 16 q^{69} + 8 q^{70} - 8 q^{71} - 3 q^{72} - 22 q^{73} + 11 q^{74} + 22 q^{75} - 72 q^{77} - 24 q^{79} - q^{80} + 19 q^{81} - 5 q^{82} - 3 q^{85} + 16 q^{86} + 20 q^{87} + 6 q^{88} - 6 q^{89} - 34 q^{90} - 2 q^{94} + 24 q^{95} + 2 q^{97} + 9 q^{98} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(338, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
338.2.c.a $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(6\) \(-1\) \(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.b $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-6\) \(3\) \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.c $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-2\) \(-1\) \(q+(-1+\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.d $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-6\) \(1\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.e $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(4\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+4\zeta_{6}q^{7}+\cdots\)
338.2.c.f $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(6\) \(-3\) \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.g $2$ $2.699$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(2\) \(1\) \(q+(1-\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
338.2.c.h $6$ $2.699$ 6.0.64827.1 None \(-3\) \(-3\) \(4\) \(4\) \(q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
338.2.c.i $6$ $2.699$ 6.0.64827.1 None \(3\) \(-3\) \(-4\) \(-4\) \(q+(1-\beta _{5})q^{2}+(-1-\beta _{1}+\beta _{4}+\beta _{5})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(338, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(338, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)