Properties

Label 335.2.a
Level 335
Weight 2
Character orbit a
Rep. character \(\chi_{335}(1,\cdot)\)
Character field \(\Q\)
Dimension 23
Newforms 5
Sturm bound 68
Trace bound 2

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Defining parameters

Level: \( N \) = \( 335 = 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 335.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(68\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(335))\).

Total New Old
Modular forms 36 23 13
Cusp forms 33 23 10
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.

\(5\)\(67\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(3\)
Minus space\(-\)\(20\)

Trace form

\(23q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 31q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 25q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 31q^{9} \) \(\mathstrut -\mathstrut 3q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 32q^{22} \) \(\mathstrut -\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut -\mathstrut 26q^{26} \) \(\mathstrut -\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 36q^{28} \) \(\mathstrut +\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut 21q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 10q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 29q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 36q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 40q^{42} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 16q^{44} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut -\mathstrut 68q^{48} \) \(\mathstrut +\mathstrut 51q^{49} \) \(\mathstrut +\mathstrut 3q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut +\mathstrut 10q^{52} \) \(\mathstrut +\mathstrut 26q^{53} \) \(\mathstrut -\mathstrut 24q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 72q^{56} \) \(\mathstrut +\mathstrut 48q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 28q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut -\mathstrut 32q^{62} \) \(\mathstrut +\mathstrut 33q^{64} \) \(\mathstrut -\mathstrut 10q^{65} \) \(\mathstrut -\mathstrut 96q^{66} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut -\mathstrut 26q^{68} \) \(\mathstrut -\mathstrut 40q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut -\mathstrut 105q^{72} \) \(\mathstrut +\mathstrut 36q^{73} \) \(\mathstrut -\mathstrut 26q^{74} \) \(\mathstrut +\mathstrut 4q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 40q^{77} \) \(\mathstrut -\mathstrut 96q^{78} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut -\mathstrut 58q^{82} \) \(\mathstrut -\mathstrut 60q^{83} \) \(\mathstrut -\mathstrut 126q^{84} \) \(\mathstrut -\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 38q^{86} \) \(\mathstrut -\mathstrut 28q^{87} \) \(\mathstrut +\mathstrut 28q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 21q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 32q^{92} \) \(\mathstrut -\mathstrut 36q^{93} \) \(\mathstrut -\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 14q^{96} \) \(\mathstrut +\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(335))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 67
335.2.a.a \(1\) \(2.675\) \(\Q\) None \(0\) \(0\) \(1\) \(-2\) \(-\) \(-\) \(q-2q^{4}+q^{5}-2q^{7}-3q^{9}-2q^{11}+\cdots\)
335.2.a.b \(2\) \(2.675\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-4\) \(+\) \(+\) \(q+\beta q^{2}-\beta q^{3}-q^{5}-2q^{6}-2q^{7}+\cdots\)
335.2.a.c \(2\) \(2.675\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-2\) \(0\) \(+\) \(-\) \(q+\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
335.2.a.d \(7\) \(2.675\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(4\) \(-7\) \(10\) \(+\) \(-\) \(q+(\beta _{2}+\beta _{5})q^{2}+(1-\beta _{4})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
335.2.a.e \(11\) \(2.675\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(0\) \(11\) \(4\) \(-\) \(+\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(335))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(335)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 2}\)