Properties

Label 334.2.a
Level 334
Weight 2
Character orbit a
Rep. character \(\chi_{334}(1,\cdot)\)
Character field \(\Q\)
Dimension 13
Newforms 6
Sturm bound 84
Trace bound 3

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Defining parameters

Level: \( N \) = \( 334 = 2 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 334.a (trivial)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(84\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(334))\).

Total New Old
Modular forms 44 13 31
Cusp forms 41 13 28
Eisenstein series 3 0 3

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

\(2\)\(167\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(9\)

Trace form

\(13q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 13q^{16} \) \(\mathstrut +\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 32q^{35} \) \(\mathstrut +\mathstrut 13q^{36} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut +\mathstrut 26q^{41} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 6q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut -\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 12q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut +\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 4q^{60} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 8q^{62} \) \(\mathstrut -\mathstrut 40q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 28q^{65} \) \(\mathstrut -\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 10q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 38q^{73} \) \(\mathstrut -\mathstrut 8q^{74} \) \(\mathstrut -\mathstrut 44q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut -\mathstrut 19q^{81} \) \(\mathstrut -\mathstrut 14q^{82} \) \(\mathstrut +\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 16q^{84} \) \(\mathstrut +\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut +\mathstrut 28q^{87} \) \(\mathstrut -\mathstrut 8q^{88} \) \(\mathstrut +\mathstrut 22q^{89} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 4q^{92} \) \(\mathstrut -\mathstrut 40q^{93} \) \(\mathstrut +\mathstrut 20q^{94} \) \(\mathstrut +\mathstrut 32q^{95} \) \(\mathstrut -\mathstrut 10q^{97} \) \(\mathstrut -\mathstrut 25q^{98} \) \(\mathstrut +\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(334))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 167
334.2.a.a \(1\) \(2.667\) \(\Q\) None \(1\) \(0\) \(3\) \(1\) \(-\) \(+\) \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
334.2.a.b \(2\) \(2.667\) \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
334.2.a.c \(2\) \(2.667\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-6\) \(+\) \(-\) \(q-q^{2}+2\beta q^{3}+q^{4}+(1-\beta )q^{5}-2\beta q^{6}+\cdots\)
334.2.a.d \(2\) \(2.667\) \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(-4\) \(-6\) \(-\) \(-\) \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-3+2\beta )q^{5}+\cdots\)
334.2.a.e \(3\) \(2.667\) 3.3.469.1 None \(-3\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
334.2.a.f \(3\) \(2.667\) 3.3.733.1 None \(3\) \(1\) \(-3\) \(3\) \(-\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(334))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(334)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 2}\)