Properties

Label 354.2.a
Level 354
Weight 2
Character orbit a
Rep. character \(\chi_{354}(1,\cdot)\)
Character field \(\Q\)
Dimension 11
Newforms 8
Sturm bound 120
Trace bound 5

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Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 354.a (trivial)
Character field: \(\Q\)
Newforms: \( 8 \)
Sturm bound: \(120\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(354))\).

Total New Old
Modular forms 64 11 53
Cusp forms 57 11 46
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.

\(2\)\(3\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(2\)
Minus space\(-\)\(9\)

Trace form

\( 11q + q^{2} + q^{3} + 11q^{4} + 6q^{5} - q^{6} + 4q^{7} + q^{8} + 11q^{9} + O(q^{10}) \) \( 11q + q^{2} + q^{3} + 11q^{4} + 6q^{5} - q^{6} + 4q^{7} + q^{8} + 11q^{9} - 2q^{10} - 4q^{11} + q^{12} + 2q^{13} - 8q^{14} + 2q^{15} + 11q^{16} - 6q^{17} + q^{18} + 4q^{19} + 6q^{20} + 8q^{21} - 8q^{23} - q^{24} + 21q^{25} + 6q^{26} + q^{27} + 4q^{28} - 18q^{29} + 2q^{30} - 4q^{31} + q^{32} + 4q^{33} - 6q^{34} - 8q^{35} + 11q^{36} + 18q^{37} - 12q^{38} + 6q^{39} - 2q^{40} + 2q^{41} - 8q^{42} - 4q^{44} + 6q^{45} - 8q^{46} + 16q^{47} + q^{48} - 9q^{49} + 15q^{50} - 6q^{51} + 2q^{52} - 26q^{53} - q^{54} - 8q^{56} + 4q^{57} + 6q^{58} - q^{59} + 2q^{60} - 6q^{61} - 16q^{62} + 4q^{63} + 11q^{64} - 36q^{65} + 4q^{66} - 32q^{67} - 6q^{68} - 16q^{69} - 24q^{70} - 40q^{71} + q^{72} - 42q^{73} - 10q^{74} - q^{75} + 4q^{76} - 32q^{77} - 10q^{78} - 28q^{79} + 6q^{80} + 11q^{81} + 10q^{82} - 20q^{83} + 8q^{84} - 12q^{85} - 20q^{86} - 6q^{87} + 26q^{89} - 2q^{90} - 8q^{92} + 12q^{93} - 8q^{94} + 16q^{95} - q^{96} - 10q^{97} - 7q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(354))\) 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 59
354.2.a.a \(1\) \(2.827\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
354.2.a.b \(1\) \(2.827\) \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
354.2.a.c \(1\) \(2.827\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
354.2.a.d \(1\) \(2.827\) \(\Q\) None \(1\) \(-1\) \(-4\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
354.2.a.e \(1\) \(2.827\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
354.2.a.f \(1\) \(2.827\) \(\Q\) None \(1\) \(-1\) \(4\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
354.2.a.g \(2\) \(2.827\) \(\Q(\sqrt{11}) \) None \(-2\) \(2\) \(2\) \(8\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
354.2.a.h \(3\) \(2.827\) 3.3.316.1 None \(3\) \(3\) \(2\) \(-1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(354))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(354)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 2}\)