Properties

Label 182.2.n
Level $182$
Weight $2$
Character orbit 182.n
Rep. character $\chi_{182}(25,\cdot)$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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

\( 16 q + 8 q^{4} + 4 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{4} + 4 q^{9} - 4 q^{10} + 4 q^{13} + 2 q^{14} - 8 q^{16} - 10 q^{17} - 4 q^{22} + 12 q^{23} + 4 q^{25} - 6 q^{26} - 12 q^{27} + 20 q^{29} - 14 q^{30} - 36 q^{35} + 8 q^{36} - 14 q^{38} - 24 q^{39} + 4 q^{40} + 8 q^{42} - 22 q^{49} - 22 q^{51} + 2 q^{52} + 2 q^{53} - 40 q^{55} + 10 q^{56} - 26 q^{61} + 12 q^{62} - 16 q^{64} + 24 q^{65} - 16 q^{66} + 10 q^{68} + 8 q^{69} - 24 q^{74} + 56 q^{75} + 48 q^{77} + 32 q^{78} - 16 q^{79} + 24 q^{81} + 8 q^{82} + 32 q^{87} - 2 q^{88} + 52 q^{90} - 8 q^{91} + 24 q^{92} + 22 q^{94} + O(q^{100}) \)

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.n.a 182.n 91.r $4$ $1.453$ \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}-2\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
182.2.n.b 182.n 91.r $12$ $1.453$ 12.0.\(\cdots\).1 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{10}q^{2}+(1-\beta _{7}+\beta _{9})q^{3}+(1-\beta _{7}+\cdots)q^{4}+\cdots\)

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

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