Properties

Label 154.2.a
Level 154
Weight 2
Character orbit a
Rep. character \(\chi_{154}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 4
Sturm bound 48
Trace bound 3

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Defining parameters

Level: \( N \) = \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 154.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(154))\).

Total New Old
Modular forms 28 5 23
Cusp forms 21 5 16
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.

\(2\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\( 5q + q^{2} + 5q^{4} + 2q^{5} - 4q^{6} - q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( 5q + q^{2} + 5q^{4} + 2q^{5} - 4q^{6} - q^{7} + q^{8} + q^{9} + 6q^{10} + q^{11} - 2q^{13} + 3q^{14} - 8q^{15} + 5q^{16} - 6q^{17} + 5q^{18} - 12q^{19} + 2q^{20} - 4q^{21} + q^{22} + 8q^{23} - 4q^{24} + 11q^{25} + 2q^{26} - 24q^{27} - q^{28} - 2q^{29} - 16q^{30} - 16q^{31} + q^{32} + 2q^{34} + 2q^{35} + q^{36} - 2q^{37} - 8q^{38} - 16q^{39} + 6q^{40} + 18q^{41} - 20q^{43} + q^{44} + 34q^{45} - 8q^{46} + 16q^{47} + 5q^{49} - 9q^{50} + 24q^{51} - 2q^{52} + 6q^{53} - 16q^{54} + 6q^{55} + 3q^{56} + 8q^{57} - 2q^{58} + 8q^{59} - 8q^{60} - 18q^{61} + 8q^{62} + 11q^{63} + 5q^{64} - 4q^{65} - 4q^{66} - 20q^{67} - 6q^{68} - 2q^{70} + 8q^{71} + 5q^{72} + 2q^{73} - 10q^{74} - 24q^{75} - 12q^{76} + 3q^{77} + 16q^{79} + 2q^{80} + 29q^{81} + 10q^{82} - 4q^{83} - 4q^{84} - 4q^{85} + 4q^{86} + 24q^{87} + q^{88} + 18q^{89} + 6q^{90} - 2q^{91} + 8q^{92} - 24q^{93} - 8q^{94} + 32q^{95} - 4q^{96} + 18q^{97} + q^{98} + 13q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(154))\) 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 11
154.2.a.a \(1\) \(1.230\) \(\Q\) None \(-1\) \(0\) \(-4\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
154.2.a.b \(1\) \(1.230\) \(\Q\) None \(-1\) \(2\) \(2\) \(-1\) \(+\) \(+\) \(-\) \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-q^{7}+\cdots\)
154.2.a.c \(1\) \(1.230\) \(\Q\) None \(1\) \(0\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
154.2.a.d \(2\) \(1.230\) \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(2\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(154))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(154)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)