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Properties

Label 102.2.a
Level $102$
Weight $2$
Character orbit 102.a
Rep. character $\chi_{102}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $36$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 102.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(102))\).

Total New Old
Modular forms 22 3 19
Cusp forms 15 3 12
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.

\(2\)\(3\)\(17\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(-\)\(+\)$-$\(1\)
\(-\)\(-\)\(-\)$-$\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(102))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 17
102.2.a.a 102.a 1.a $1$ $0.814$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)
102.2.a.b 102.a 1.a $1$ $0.814$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
102.2.a.c 102.a 1.a $1$ $0.814$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(102))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(102)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)