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Properties

Label 102.4.a
Level $102$
Weight $4$
Character orbit 102.a
Rep. character $\chi_{102}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $6$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 102 = 2 \cdot 3 \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 102.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(72\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(102))\).

Total New Old
Modular forms 58 8 50
Cusp forms 50 8 42
Eisenstein series 8 0 8

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
\(+\)\(+\)\(-\)$-$\(1\)
\(+\)\(-\)\(+\)$-$\(1\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(+\)$+$\(2\)
Plus space\(+\)\(5\)
Minus space\(-\)\(3\)

Trace form

\( 8 q + 6 q^{3} + 32 q^{4} - 12 q^{6} + 16 q^{7} + 72 q^{9} + O(q^{10}) \) \( 8 q + 6 q^{3} + 32 q^{4} - 12 q^{6} + 16 q^{7} + 72 q^{9} - 16 q^{10} - 56 q^{11} + 24 q^{12} + 4 q^{13} + 16 q^{14} + 60 q^{15} + 128 q^{16} + 92 q^{19} - 12 q^{21} + 80 q^{22} - 504 q^{23} - 48 q^{24} - 44 q^{25} + 224 q^{26} + 54 q^{27} + 64 q^{28} - 64 q^{29} + 584 q^{31} + 204 q^{33} - 136 q^{34} - 320 q^{35} + 288 q^{36} - 960 q^{37} - 240 q^{38} + 252 q^{39} - 64 q^{40} - 1200 q^{41} + 408 q^{42} + 620 q^{43} - 224 q^{44} + 336 q^{46} - 760 q^{47} + 96 q^{48} + 944 q^{49} - 432 q^{50} - 102 q^{51} + 16 q^{52} - 328 q^{53} - 108 q^{54} - 124 q^{55} + 64 q^{56} + 192 q^{57} - 144 q^{58} - 840 q^{59} + 240 q^{60} - 656 q^{61} - 1424 q^{62} + 144 q^{63} + 512 q^{64} + 1088 q^{65} - 240 q^{66} + 24 q^{67} + 144 q^{69} + 496 q^{70} - 168 q^{71} - 1032 q^{73} + 256 q^{74} + 1050 q^{75} + 368 q^{76} + 24 q^{77} - 312 q^{78} + 2144 q^{79} + 648 q^{81} - 784 q^{82} + 560 q^{83} - 48 q^{84} + 476 q^{85} + 800 q^{86} + 720 q^{87} + 320 q^{88} + 344 q^{89} - 144 q^{90} + 3192 q^{91} - 2016 q^{92} + 492 q^{93} - 928 q^{94} + 2976 q^{95} - 192 q^{96} - 2168 q^{97} - 752 q^{98} - 504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(102))\) 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
102.4.a.a 102.a 1.a $1$ $6.018$ \(\Q\) None \(-2\) \(-3\) \(-3\) \(20\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-3q^{5}+6q^{6}+\cdots\)
102.4.a.b 102.a 1.a $1$ $6.018$ \(\Q\) None \(-2\) \(3\) \(-5\) \(-32\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
102.4.a.c 102.a 1.a $1$ $6.018$ \(\Q\) None \(2\) \(-3\) \(-12\) \(-22\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-12q^{5}-6q^{6}+\cdots\)
102.4.a.d 102.a 1.a $1$ $6.018$ \(\Q\) None \(2\) \(-3\) \(5\) \(12\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
102.4.a.e 102.a 1.a $2$ $6.018$ \(\Q(\sqrt{15}) \) None \(-4\) \(6\) \(12\) \(16\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(6+\beta )q^{5}-6q^{6}+\cdots\)
102.4.a.f 102.a 1.a $2$ $6.018$ \(\Q(\sqrt{393}) \) None \(4\) \(6\) \(3\) \(22\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(2-\beta )q^{5}+6q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(102))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(102)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)