Properties

Label 182.2.a
Level 182
Weight 2
Character orbit a
Rep. character \(\chi_{182}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 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: \(\Q\)
Newforms: \( 5 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(182))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 13
182.2.a.a \(1\) \(1.453\) \(\Q\) None \(-1\) \(1\) \(4\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
182.2.a.b \(1\) \(1.453\) \(\Q\) None \(-1\) \(3\) \(0\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}-3q^{6}+q^{7}-q^{8}+\cdots\)
182.2.a.c \(1\) \(1.453\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
182.2.a.d \(1\) \(1.453\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
182.2.a.e \(1\) \(1.453\) \(\Q\) None \(1\) \(3\) \(-4\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+3q^{3}+q^{4}-4q^{5}+3q^{6}-q^{7}+\cdots\)

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

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