Properties

Label 1339.2.a
Level $1339$
Weight $2$
Character orbit 1339.a
Rep. character $\chi_{1339}(1,\cdot)$
Character field $\Q$
Dimension $103$
Newform subspaces $7$
Sturm bound $242$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(242\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1339))\).

Total New Old
Modular forms 122 103 19
Cusp forms 119 103 16
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.

\(13\)\(103\)FrickeDim.
\(+\)\(+\)\(+\)\(22\)
\(+\)\(-\)\(-\)\(30\)
\(-\)\(+\)\(-\)\(29\)
\(-\)\(-\)\(+\)\(22\)
Plus space\(+\)\(44\)
Minus space\(-\)\(59\)

Trace form

\( 103q - 3q^{2} + 97q^{4} + 2q^{5} - 3q^{8} + 103q^{9} + O(q^{10}) \) \( 103q - 3q^{2} + 97q^{4} + 2q^{5} - 3q^{8} + 103q^{9} + 10q^{10} - 4q^{11} + 16q^{12} - q^{13} + 16q^{14} + 4q^{15} + 81q^{16} - 14q^{17} + 9q^{18} - 16q^{19} + 26q^{20} + 8q^{21} - 4q^{22} - 16q^{23} + 24q^{24} + 125q^{25} - 3q^{26} - 12q^{27} - 20q^{28} + 6q^{29} - 12q^{30} + 16q^{31} - 19q^{32} - 12q^{33} - 54q^{34} - 16q^{35} + 73q^{36} + 6q^{37} + 36q^{38} + 4q^{39} + 10q^{40} - 18q^{41} - 48q^{42} - 20q^{43} - 36q^{44} + 14q^{45} - 24q^{46} + 24q^{47} + 20q^{48} + 111q^{49} - 53q^{50} - 24q^{51} + q^{52} + 2q^{53} - 52q^{54} - 4q^{55} - 12q^{56} - 36q^{57} - 14q^{58} - 16q^{59} - 60q^{60} - 14q^{61} - 88q^{62} - 12q^{63} + 5q^{64} + 2q^{65} - 84q^{66} - 16q^{67} - 18q^{68} + 32q^{69} + 48q^{70} + 16q^{71} - 39q^{72} + 10q^{73} + 6q^{74} + 4q^{75} - 64q^{76} - 40q^{77} + 12q^{78} + 4q^{79} + 86q^{80} + 111q^{81} + 22q^{82} - 4q^{83} - 100q^{84} - 24q^{86} + 20q^{87} - 16q^{88} + 78q^{89} + 22q^{90} - 8q^{91} - 76q^{92} + 76q^{93} - 36q^{94} + 16q^{95} - 4q^{96} - 6q^{97} + 17q^{98} - 28q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1339))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 13 103
1339.2.a.a \(1\) \(10.692\) \(\Q\) None \(1\) \(-1\) \(1\) \(4\) \(+\) \(+\) \(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\)
1339.2.a.b \(1\) \(10.692\) \(\Q\) None \(1\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(q+q^{2}-q^{4}-4q^{7}-3q^{8}-3q^{9}+6q^{11}+\cdots\)
1339.2.a.c \(3\) \(10.692\) 3.3.148.1 None \(-1\) \(-1\) \(-7\) \(2\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
1339.2.a.d \(19\) \(10.692\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(-9\) \(-2\) \(-18\) \(-8\) \(-\) \(-\) \(q-\beta _{1}q^{2}-\beta _{14}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1339.2.a.e \(21\) \(10.692\) None \(-1\) \(-6\) \(-18\) \(-2\) \(+\) \(+\)
1339.2.a.f \(28\) \(10.692\) None \(6\) \(5\) \(27\) \(6\) \(-\) \(+\)
1339.2.a.g \(30\) \(10.692\) None \(0\) \(5\) \(17\) \(2\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1339))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1339)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(103))\)\(^{\oplus 2}\)