Properties

Label 182.2.a
Level $182$
Weight $2$
Character orbit 182.a
Rep. character $\chi_{182}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $56$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 182.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(182))\).

Total New Old
Modular forms 32 5 27
Cusp forms 25 5 20
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)\(13\)FrickeDim
\(+\)\(+\)\(-\)$-$\(1\)
\(+\)\(-\)\(+\)$-$\(1\)
\(-\)\(+\)\(+\)$-$\(2\)
\(-\)\(-\)\(-\)$-$\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(5\)

Trace form

\( 5 q + q^{2} + 8 q^{3} + 5 q^{4} + 2 q^{5} - q^{7} + q^{8} + 5 q^{9} + O(q^{10}) \) \( 5 q + q^{2} + 8 q^{3} + 5 q^{4} + 2 q^{5} - q^{7} + q^{8} + 5 q^{9} - 6 q^{10} - 4 q^{11} + 8 q^{12} - q^{13} - q^{14} - 8 q^{15} + 5 q^{16} - 6 q^{17} - 3 q^{18} + 2 q^{20} + 8 q^{22} - 4 q^{23} + 11 q^{25} - q^{26} + 8 q^{27} - q^{28} - 18 q^{29} - 16 q^{30} + 8 q^{31} + q^{32} - 16 q^{33} - 6 q^{34} - 2 q^{35} + 5 q^{36} + 22 q^{37} - 8 q^{38} - 4 q^{39} - 6 q^{40} - 22 q^{41} - 4 q^{42} - 4 q^{43} - 4 q^{44} - 38 q^{45} - 8 q^{47} + 8 q^{48} + 5 q^{49} - q^{50} - 8 q^{51} - q^{52} - 10 q^{53} - q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 8 q^{60} + 10 q^{61} + 3 q^{63} + 5 q^{64} + 6 q^{65} + 16 q^{66} + 28 q^{67} - 6 q^{68} - 16 q^{69} + 6 q^{70} + 24 q^{71} - 3 q^{72} + 34 q^{73} - 6 q^{74} + 24 q^{75} - 12 q^{77} - 12 q^{79} + 2 q^{80} + 29 q^{81} + 10 q^{82} + 4 q^{85} + 36 q^{86} - 8 q^{87} + 8 q^{88} + 2 q^{89} - 22 q^{90} + q^{91} - 4 q^{92} + 32 q^{93} + 32 q^{95} + 34 q^{97} + q^{98} - 28 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(182))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7 13
182.2.a.a 182.a 1.a $1$ $1.453$ \(\Q\) None 182.2.a.a \(-1\) \(1\) \(4\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
182.2.a.b 182.a 1.a $1$ $1.453$ \(\Q\) None 182.2.a.b \(-1\) \(3\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots\)
182.2.a.c 182.a 1.a $1$ $1.453$ \(\Q\) None 182.2.a.c \(1\) \(0\) \(2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
182.2.a.d 182.a 1.a $1$ $1.453$ \(\Q\) None 182.2.a.d \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
182.2.a.e 182.a 1.a $1$ $1.453$ \(\Q\) None 182.2.a.e \(1\) \(3\) \(-4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}-4q^{5}+3q^{6}-q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(182))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(182)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)