Properties

Label 182.2.h
Level $182$
Weight $2$
Character orbit 182.h
Rep. character $\chi_{182}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $4$
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.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
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 20 44
Cusp forms 48 20 28
Eisenstein series 16 0 16

Trace form

\( 20 q + 4 q^{3} - 10 q^{4} - 6 q^{7} + 16 q^{9} + O(q^{10}) \) \( 20 q + 4 q^{3} - 10 q^{4} - 6 q^{7} + 16 q^{9} + 8 q^{10} + 20 q^{11} - 2 q^{12} - 6 q^{13} - 4 q^{15} - 10 q^{16} - 6 q^{17} - 6 q^{21} + 2 q^{22} - 18 q^{25} + 6 q^{26} + 4 q^{27} + 12 q^{28} + 2 q^{29} - 20 q^{30} - 22 q^{31} - 32 q^{33} - 24 q^{35} - 8 q^{36} + 20 q^{37} - 10 q^{38} - 2 q^{39} - 4 q^{40} - 2 q^{41} + 4 q^{42} + 8 q^{43} - 10 q^{44} + 20 q^{45} + 8 q^{46} + 6 q^{47} - 2 q^{48} - 4 q^{49} + 12 q^{50} + 14 q^{51} - 8 q^{53} - 6 q^{54} + 2 q^{55} + 6 q^{56} - 28 q^{57} - 8 q^{59} - 4 q^{60} + 48 q^{61} - 20 q^{62} - 24 q^{63} + 20 q^{64} - 50 q^{65} - 16 q^{66} - 6 q^{68} - 26 q^{69} + 40 q^{70} - 26 q^{71} + 28 q^{73} + 30 q^{75} - 10 q^{77} - 12 q^{78} - 10 q^{79} - 44 q^{81} + 32 q^{82} + 84 q^{83} + 20 q^{85} + 10 q^{86} - 40 q^{87} - 4 q^{88} - 14 q^{89} + 28 q^{90} + 48 q^{91} + 4 q^{93} + 64 q^{94} + 4 q^{95} + 34 q^{97} - 36 q^{98} + 52 q^{99} + O(q^{100}) \)

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.h.a 182.h 91.g $2$ $1.453$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+q^{3}+(-1+\zeta_{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
182.2.h.b 182.h 91.g $2$ $1.453$ \(\Q(\sqrt{-3}) \) None \(1\) \(2\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+q^{3}+(-1+\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
182.2.h.c 182.h 91.g $6$ $1.453$ 6.0.4740147.1 None \(3\) \(-2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{1})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots\)
182.2.h.d 182.h 91.g $10$ $1.453$ 10.0.\(\cdots\).1 None \(-5\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-\beta _{4}+\beta _{5})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)

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

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