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Properties

Label 182.2.f
Level $182$
Weight $2$
Character orbit 182.f
Rep. character $\chi_{182}(53,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $3$
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.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
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

\( 16 q - 8 q^{4} + 8 q^{7} - 12 q^{9} + O(q^{10}) \) \( 16 q - 8 q^{4} + 8 q^{7} - 12 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{13} - 6 q^{14} + 32 q^{15} - 8 q^{16} - 6 q^{17} + 4 q^{19} - 16 q^{21} - 4 q^{22} - 12 q^{23} - 4 q^{25} + 6 q^{26} - 12 q^{27} - 4 q^{28} + 20 q^{29} - 2 q^{30} - 12 q^{31} + 28 q^{33} + 12 q^{35} + 24 q^{36} - 10 q^{38} - 4 q^{40} - 32 q^{41} - 8 q^{42} + 48 q^{43} - 4 q^{44} - 40 q^{45} - 4 q^{46} - 12 q^{47} + 22 q^{49} + 48 q^{50} - 10 q^{51} + 2 q^{52} + 10 q^{53} + 12 q^{54} - 40 q^{55} + 6 q^{56} + 48 q^{57} - 24 q^{58} - 8 q^{59} - 16 q^{60} - 2 q^{61} + 4 q^{62} - 4 q^{63} + 16 q^{64} + 4 q^{65} - 16 q^{66} - 8 q^{67} - 6 q^{68} - 56 q^{69} - 8 q^{70} - 8 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{76} + 32 q^{77} - 24 q^{79} - 24 q^{81} + 8 q^{82} - 24 q^{83} + 32 q^{84} + 32 q^{85} + 4 q^{86} - 16 q^{87} + 2 q^{88} + 28 q^{89} + 28 q^{90} - 16 q^{91} + 24 q^{92} + 20 q^{93} + 22 q^{94} + 16 q^{95} + 32 q^{97} - 24 q^{98} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
182.2.f.a 182.f 7.c $2$ $1.453$ \(\Q(\sqrt{-3}) \) None 182.2.f.a \(1\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
182.2.f.b 182.f 7.c $6$ $1.453$ 6.0.309123.1 None 182.2.f.b \(3\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
182.2.f.c 182.f 7.c $8$ $1.453$ 8.0.8681953329.1 None 182.2.f.c \(-4\) \(0\) \(-2\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{7})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)

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

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