Properties

Label 1335.2.a
Level 1335
Weight 2
Character orbit a
Rep. character \(\chi_{1335}(1,\cdot)\)
Character field \(\Q\)
Dimension 59
Newforms 11
Sturm bound 360
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1335 = 3 \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1335.a (trivial)
Character field: \(\Q\)
Newforms: \( 11 \)
Sturm bound: \(360\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1335))\).

Total New Old
Modular forms 184 59 125
Cusp forms 177 59 118
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.

\(3\)\(5\)\(89\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(13\)
Plus space\(+\)\(16\)
Minus space\(-\)\(43\)

Trace form

\(59q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 59q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(59q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 59q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut +\mathstrut 18q^{13} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 77q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 7q^{20} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 59q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 32q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 73q^{32} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 42q^{37} \) \(\mathstrut +\mathstrut 52q^{38} \) \(\mathstrut +\mathstrut 10q^{39} \) \(\mathstrut -\mathstrut 3q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 36q^{44} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut -\mathstrut 3q^{48} \) \(\mathstrut +\mathstrut 83q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut +\mathstrut 38q^{52} \) \(\mathstrut +\mathstrut 58q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 50q^{58} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 5q^{60} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 8q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut -\mathstrut 4q^{66} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut -\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut -\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 36q^{76} \) \(\mathstrut -\mathstrut 42q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut q^{80} \) \(\mathstrut +\mathstrut 59q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut +\mathstrut 56q^{84} \) \(\mathstrut +\mathstrut 6q^{85} \) \(\mathstrut +\mathstrut 36q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 60q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut +\mathstrut q^{90} \) \(\mathstrut -\mathstrut 48q^{91} \) \(\mathstrut -\mathstrut 32q^{92} \) \(\mathstrut +\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 35q^{96} \) \(\mathstrut -\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 35q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1335))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 89
1335.2.a.a \(1\) \(10.660\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
1335.2.a.b \(1\) \(10.660\) \(\Q\) None \(1\) \(1\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
1335.2.a.c \(2\) \(10.660\) \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
1335.2.a.d \(3\) \(10.660\) \(\Q(\zeta_{14})^+\) None \(-2\) \(3\) \(3\) \(-5\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
1335.2.a.e \(3\) \(10.660\) \(\Q(\zeta_{18})^+\) None \(0\) \(-3\) \(3\) \(3\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
1335.2.a.f \(4\) \(10.660\) 4.4.2777.1 None \(0\) \(4\) \(-4\) \(-7\) \(-\) \(+\) \(-\) \(q+\beta _{2}q^{2}+q^{3}+(1-\beta _{3})q^{4}-q^{5}+\beta _{2}q^{6}+\cdots\)
1335.2.a.g \(6\) \(10.660\) 6.6.10407557.1 None \(-4\) \(-6\) \(-6\) \(1\) \(+\) \(+\) \(+\) \(q+(-1-\beta _{2})q^{2}-q^{3}+(2+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
1335.2.a.h \(9\) \(10.660\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(5\) \(-9\) \(-9\) \(-3\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1335.2.a.i \(10\) \(10.660\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(-10\) \(9\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
1335.2.a.j \(10\) \(10.660\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(1\) \(-10\) \(10\) \(-1\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1335.2.a.k \(10\) \(10.660\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(6\) \(10\) \(10\) \(7\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1335))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1335)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(445))\)\(^{\oplus 2}\)