Properties

Label 182.2.g
Level $182$
Weight $2$
Character orbit 182.g
Rep. character $\chi_{182}(29,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $5$
Sturm bound $56$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(56\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(182, [\chi])\).

Total New Old
Modular forms 64 12 52
Cusp forms 48 12 36
Eisenstein series 16 0 16

Trace form

\( 12 q + 2 q^{2} - 6 q^{4} + 4 q^{5} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 12 q + 2 q^{2} - 6 q^{4} + 4 q^{5} - 4 q^{8} - 6 q^{9} - 6 q^{10} + 4 q^{11} - 6 q^{13} - 8 q^{14} - 4 q^{15} - 6 q^{16} - 6 q^{17} - 12 q^{18} + 16 q^{19} - 2 q^{20} + 8 q^{21} + 4 q^{22} - 8 q^{23} + 24 q^{25} + 10 q^{26} + 24 q^{27} - 6 q^{29} - 8 q^{30} + 8 q^{31} + 2 q^{32} - 32 q^{33} - 12 q^{34} + 8 q^{35} - 6 q^{36} - 6 q^{37} + 32 q^{38} + 12 q^{40} - 14 q^{41} + 4 q^{42} - 4 q^{43} - 8 q^{44} + 26 q^{45} - 12 q^{46} - 16 q^{47} - 6 q^{49} + 4 q^{50} + 56 q^{51} - 20 q^{53} + 12 q^{54} - 12 q^{55} + 4 q^{56} - 24 q^{57} - 2 q^{58} - 16 q^{59} + 8 q^{60} - 18 q^{61} - 12 q^{62} - 4 q^{63} + 12 q^{64} - 18 q^{65} - 16 q^{66} - 12 q^{67} - 6 q^{68} + 4 q^{69} + 6 q^{72} - 36 q^{73} + 30 q^{74} - 40 q^{75} + 16 q^{76} + 12 q^{78} + 40 q^{79} - 2 q^{80} + 30 q^{81} - 10 q^{82} - 24 q^{83} - 4 q^{84} - 34 q^{85} + 24 q^{86} + 20 q^{87} + 4 q^{88} + 28 q^{89} + 52 q^{90} + 4 q^{91} + 16 q^{92} - 40 q^{93} + 4 q^{95} + 12 q^{97} + 2 q^{98} + 40 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(182, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
182.2.g.a $2$ $1.453$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-6\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
182.2.g.b $2$ $1.453$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(6\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
182.2.g.c $2$ $1.453$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-6\) \(-1\) \(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
182.2.g.d $2$ $1.453$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(2\) \(1\) \(q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
182.2.g.e $4$ $1.453$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(8\) \(2\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(182, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(182, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)