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Properties

Label 277.2.a
Level $277$
Weight $2$
Character orbit 277.a
Rep. character $\chi_{277}(1,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $4$
Sturm bound $46$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 277.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(46\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(277))\).

Total New Old
Modular forms 23 23 0
Cusp forms 22 22 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.

\(277\)Dim
\(+\)\(10\)
\(-\)\(12\)

Trace form

\( 22 q - 2 q^{2} + 20 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 26 q^{9} + O(q^{10}) \) \( 22 q - 2 q^{2} + 20 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{8} + 26 q^{9} - 4 q^{10} - 14 q^{12} - 8 q^{13} - 10 q^{14} + 10 q^{15} + 4 q^{16} - 6 q^{17} - 18 q^{18} - 2 q^{19} - 22 q^{20} - 4 q^{21} - 26 q^{22} - 12 q^{23} - 8 q^{24} + 14 q^{25} - 2 q^{26} - 12 q^{28} - 4 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} + 6 q^{34} - 6 q^{35} + 54 q^{36} - 16 q^{37} + 12 q^{38} - 10 q^{39} + 8 q^{40} - 6 q^{41} + 34 q^{42} - 20 q^{43} + 18 q^{44} - 22 q^{45} + 22 q^{46} + 24 q^{47} - 16 q^{48} + 10 q^{49} - 12 q^{50} + 18 q^{51} - 10 q^{52} - 12 q^{53} + 2 q^{54} + 4 q^{55} - 22 q^{56} + 10 q^{57} + 28 q^{58} - 14 q^{59} + 34 q^{60} - 6 q^{61} + 50 q^{62} - 44 q^{63} - 34 q^{64} + 6 q^{65} + 4 q^{66} + 2 q^{67} - 6 q^{68} + 68 q^{69} + 30 q^{70} - 14 q^{71} - 4 q^{72} - 22 q^{73} - 26 q^{74} - 38 q^{75} + 26 q^{76} - 14 q^{77} - 30 q^{78} - 8 q^{79} + 2 q^{80} + 78 q^{81} + 40 q^{82} - 26 q^{83} - 46 q^{84} - 42 q^{85} + 58 q^{86} - 52 q^{87} - 34 q^{88} - 8 q^{89} - 40 q^{90} - 56 q^{91} - 32 q^{92} - 16 q^{93} - 22 q^{94} - 22 q^{95} + 40 q^{96} + 6 q^{97} - 12 q^{98} + 26 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(277))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 277
277.2.a.a 277.a 1.a $1$ $2.212$ \(\Q\) None \(1\) \(-2\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}-q^{4}+2q^{5}-2q^{6}-4q^{7}+\cdots\)
277.2.a.b 277.a 1.a $3$ $2.212$ 3.3.148.1 None \(-1\) \(6\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+2q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
277.2.a.c 277.a 1.a $9$ $2.212$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-6\) \(-10\) \(-12\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(-1-\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
277.2.a.d 277.a 1.a $9$ $2.212$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(4\) \(6\) \(4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{4}+\beta _{8})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots\)