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Properties

Label 182.2.m
Level $182$
Weight $2$
Character orbit 182.m
Rep. character $\chi_{182}(43,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $2$
Sturm bound $56$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 64 16 48
Cusp forms 48 16 32
Eisenstein series 16 0 16

Trace form

\( 16 q + 8 q^{4} - 8 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{4} - 8 q^{9} - 4 q^{10} - 12 q^{11} - 8 q^{13} + 8 q^{14} - 12 q^{15} - 8 q^{16} - 4 q^{17} - 4 q^{22} - 8 q^{25} + 24 q^{27} - 4 q^{29} + 16 q^{30} + 24 q^{33} + 8 q^{36} + 12 q^{37} + 16 q^{38} - 48 q^{39} - 8 q^{40} - 36 q^{41} - 4 q^{42} + 12 q^{43} + 60 q^{45} - 12 q^{46} + 8 q^{49} - 12 q^{50} - 40 q^{51} - 4 q^{52} + 56 q^{53} - 36 q^{54} - 4 q^{55} + 4 q^{56} + 24 q^{58} - 8 q^{61} + 12 q^{62} - 12 q^{63} - 16 q^{64} - 24 q^{65} - 16 q^{66} - 12 q^{67} + 4 q^{68} + 20 q^{69} - 12 q^{72} - 40 q^{75} - 4 q^{78} + 8 q^{79} - 36 q^{81} + 8 q^{82} + 12 q^{84} + 60 q^{85} - 4 q^{87} + 4 q^{88} + 16 q^{90} - 20 q^{91} + 48 q^{93} + 16 q^{94} + 36 q^{95} + 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
182.2.m.a 182.m 13.e $4$ $1.453$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{3}+\cdots\)
182.2.m.b 182.m 13.e $12$ $1.453$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+(\beta _{2}+\beta _{10})q^{3}+(1-\beta _{7})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(182, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)