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Properties

Label 751.2.a
Level $751$
Weight $2$
Character orbit 751.a
Rep. character $\chi_{751}(1,\cdot)$
Character field $\Q$
Dimension $62$
Newform subspaces $2$
Sturm bound $125$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 751.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(125\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(751))\).

Total New Old
Modular forms 63 63 0
Cusp forms 62 62 0
Eisenstein series 1 1 0

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

\(751\)Dim
\(+\)\(24\)
\(-\)\(38\)

Trace form

\( 62 q - q^{2} - 2 q^{3} + 57 q^{4} + 2 q^{5} - 6 q^{7} - 3 q^{8} + 62 q^{9} + O(q^{10}) \) \( 62 q - q^{2} - 2 q^{3} + 57 q^{4} + 2 q^{5} - 6 q^{7} - 3 q^{8} + 62 q^{9} - 10 q^{10} - 2 q^{11} - 6 q^{12} + 2 q^{13} - 2 q^{14} - 14 q^{15} + 35 q^{16} + 10 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 6 q^{21} - 6 q^{22} - 8 q^{23} + 22 q^{24} + 60 q^{25} - 4 q^{26} + 4 q^{27} - 36 q^{28} + 4 q^{29} + 2 q^{30} - 22 q^{31} + 3 q^{32} - 8 q^{34} + 4 q^{35} + 47 q^{36} + 6 q^{37} - 6 q^{38} - 16 q^{39} - 52 q^{40} + 18 q^{41} + 4 q^{42} - 6 q^{43} + 12 q^{44} - 4 q^{45} - 32 q^{46} + 20 q^{47} - 10 q^{48} + 64 q^{49} + 15 q^{50} + 14 q^{51} + 12 q^{52} + 12 q^{53} + 60 q^{54} - 6 q^{55} - 18 q^{56} - 2 q^{57} - 28 q^{58} + 8 q^{59} - 40 q^{60} + 8 q^{61} + 24 q^{62} - 20 q^{63} + 9 q^{64} + 6 q^{65} - 36 q^{66} - 8 q^{67} + 42 q^{68} - 34 q^{69} - 32 q^{70} - 26 q^{71} - 17 q^{72} - 12 q^{73} + 72 q^{74} + 34 q^{75} - 24 q^{76} - 6 q^{77} + 18 q^{78} - 62 q^{79} + 42 q^{80} + 78 q^{81} - 12 q^{83} + 2 q^{84} + 26 q^{85} - 16 q^{86} + 38 q^{87} - 50 q^{88} + 42 q^{89} - 32 q^{90} - 14 q^{91} - 32 q^{92} - 18 q^{93} + 10 q^{94} - 4 q^{95} - 12 q^{96} + 14 q^{97} - 5 q^{98} - 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(751))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 751
751.2.a.a 751.a 1.a $24$ $5.997$ None \(-5\) \(-8\) \(-16\) \(-7\) $+$ $\mathrm{SU}(2)$
751.2.a.b 751.a 1.a $38$ $5.997$ None \(4\) \(6\) \(18\) \(1\) $-$ $\mathrm{SU}(2)$