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Properties

Label 2677.2.a
Level $2677$
Weight $2$
Character orbit 2677.a
Rep. character $\chi_{2677}(1,\cdot)$
Character field $\Q$
Dimension $222$
Newform subspaces $3$
Sturm bound $446$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2677 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2677.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(446\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2677))\).

Total New Old
Modular forms 223 223 0
Cusp forms 222 222 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.

\(2677\)Dim
\(+\)\(106\)
\(-\)\(116\)

Trace form

\( 222 q - 2 q^{3} + 222 q^{4} - 4 q^{5} - 2 q^{7} + 220 q^{9} + O(q^{10}) \) \( 222 q - 2 q^{3} + 222 q^{4} - 4 q^{5} - 2 q^{7} + 220 q^{9} - 4 q^{10} - 6 q^{11} - 12 q^{12} - 14 q^{13} + 6 q^{14} - 16 q^{15} + 226 q^{16} - 12 q^{17} - 14 q^{18} - 6 q^{19} - 12 q^{20} - 12 q^{21} + 6 q^{22} - 12 q^{23} + 2 q^{24} + 216 q^{25} + 12 q^{26} - 14 q^{27} + 2 q^{28} + 4 q^{29} + 4 q^{30} - 2 q^{31} + 30 q^{32} + 4 q^{33} + 10 q^{34} + 2 q^{35} + 220 q^{36} - 16 q^{37} - 10 q^{38} - 28 q^{39} + 4 q^{40} - 8 q^{41} + 20 q^{42} - 18 q^{43} + 2 q^{44} - 34 q^{45} + 46 q^{46} + 4 q^{47} - 36 q^{48} + 202 q^{49} - 4 q^{50} + 4 q^{51} - 52 q^{52} - 8 q^{53} + 40 q^{54} - 22 q^{55} + 4 q^{56} + 2 q^{59} - 52 q^{60} - 16 q^{61} - 2 q^{62} - 4 q^{63} + 248 q^{64} - 40 q^{65} + 22 q^{66} - 6 q^{67} - 66 q^{68} + 6 q^{69} + 58 q^{70} - 20 q^{71} - 32 q^{72} - 18 q^{73} - 4 q^{74} - 50 q^{75} + 30 q^{76} - 36 q^{77} - 66 q^{78} + 20 q^{79} - 86 q^{80} + 214 q^{81} - 8 q^{82} + 8 q^{83} - 36 q^{84} - 26 q^{85} + 84 q^{86} - 36 q^{87} + 20 q^{88} + 28 q^{89} - 48 q^{90} - 44 q^{91} - 86 q^{92} - 20 q^{93} - 18 q^{94} + 4 q^{95} + 84 q^{96} + 6 q^{97} - 16 q^{98} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2677))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2677
2677.2.a.a 2677.a 1.a $1$ $21.376$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
2677.2.a.b 2677.a 1.a $106$ $21.376$ None \(-28\) \(-29\) \(-19\) \(-27\) $+$ $\mathrm{SU}(2)$
2677.2.a.c 2677.a 1.a $115$ $21.376$ None \(29\) \(28\) \(17\) \(27\) $-$ $\mathrm{SU}(2)$