Properties

Label 366.2.a
Level 366
Weight 2
Character orbit a
Rep. character \(\chi_{366}(1,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 8
Sturm bound 124
Trace bound 7

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Defining parameters

Level: \( N \) = \( 366 = 2 \cdot 3 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 366.a (trivial)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(124\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(366))\).

Total New Old
Modular forms 66 9 57
Cusp forms 59 9 50
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.

\(2\)\(3\)\(61\)FrickeDim.
\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(7\)

Trace form

\(9q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 6q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 14q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 22q^{41} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 11q^{49} \) \(\mathstrut -\mathstrut 31q^{50} \) \(\mathstrut -\mathstrut 14q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut -\mathstrut 18q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 5q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 40q^{67} \) \(\mathstrut -\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut q^{72} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 30q^{74} \) \(\mathstrut -\mathstrut 31q^{75} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 36q^{77} \) \(\mathstrut +\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 18q^{82} \) \(\mathstrut +\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 4q^{84} \) \(\mathstrut -\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut -\mathstrut 2q^{87} \) \(\mathstrut +\mathstrut 22q^{89} \) \(\mathstrut +\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 20q^{93} \) \(\mathstrut +\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 9q^{98} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(366))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 61
366.2.a.a \(1\) \(2.923\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(4\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+4q^{7}+\cdots\)
366.2.a.b \(1\) \(2.923\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
366.2.a.c \(1\) \(2.923\) \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
366.2.a.d \(1\) \(2.923\) \(\Q\) None \(1\) \(-1\) \(-3\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
366.2.a.e \(1\) \(2.923\) \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
366.2.a.f \(1\) \(2.923\) \(\Q\) None \(1\) \(1\) \(1\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
366.2.a.g \(1\) \(2.923\) \(\Q\) None \(1\) \(1\) \(1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
366.2.a.h \(2\) \(2.923\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(0\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1-2\beta )q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(366))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(366)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 2}\)