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Properties

Label 10.8.a
Level $10$
Weight $8$
Character orbit 10.a
Rep. character $\chi_{10}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 10.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(10))\).

Total New Old
Modular forms 13 1 12
Cusp forms 9 1 8
Eisenstein series 4 0 4

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

\(2\)\(5\)FrickeDim
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\( q + 8 q^{2} + 28 q^{3} + 64 q^{4} + 125 q^{5} + 224 q^{6} + 104 q^{7} + 512 q^{8} - 1403 q^{9} + O(q^{10}) \) \( q + 8 q^{2} + 28 q^{3} + 64 q^{4} + 125 q^{5} + 224 q^{6} + 104 q^{7} + 512 q^{8} - 1403 q^{9} + 1000 q^{10} - 5148 q^{11} + 1792 q^{12} - 8602 q^{13} + 832 q^{14} + 3500 q^{15} + 4096 q^{16} + 20274 q^{17} - 11224 q^{18} + 45500 q^{19} + 8000 q^{20} + 2912 q^{21} - 41184 q^{22} - 72072 q^{23} + 14336 q^{24} + 15625 q^{25} - 68816 q^{26} - 100520 q^{27} + 6656 q^{28} + 231510 q^{29} + 28000 q^{30} - 80128 q^{31} + 32768 q^{32} - 144144 q^{33} + 162192 q^{34} + 13000 q^{35} - 89792 q^{36} + 104654 q^{37} + 364000 q^{38} - 240856 q^{39} + 64000 q^{40} + 584922 q^{41} + 23296 q^{42} - 795532 q^{43} - 329472 q^{44} - 175375 q^{45} - 576576 q^{46} + 425664 q^{47} + 114688 q^{48} - 812727 q^{49} + 125000 q^{50} + 567672 q^{51} - 550528 q^{52} + 1500798 q^{53} - 804160 q^{54} - 643500 q^{55} + 53248 q^{56} + 1274000 q^{57} + 1852080 q^{58} + 246420 q^{59} + 224000 q^{60} + 893942 q^{61} - 641024 q^{62} - 145912 q^{63} + 262144 q^{64} - 1075250 q^{65} - 1153152 q^{66} - 2336836 q^{67} + 1297536 q^{68} - 2018016 q^{69} + 104000 q^{70} - 203688 q^{71} - 718336 q^{72} - 3805702 q^{73} + 837232 q^{74} + 437500 q^{75} + 2912000 q^{76} - 535392 q^{77} - 1926848 q^{78} + 5053040 q^{79} + 512000 q^{80} + 253801 q^{81} + 4679376 q^{82} - 45492 q^{83} + 186368 q^{84} + 2534250 q^{85} - 6364256 q^{86} + 6482280 q^{87} - 2635776 q^{88} + 980010 q^{89} - 1403000 q^{90} - 894608 q^{91} - 4612608 q^{92} - 2243584 q^{93} + 3405312 q^{94} + 5687500 q^{95} + 917504 q^{96} - 5247646 q^{97} - 6501816 q^{98} + 7222644 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(10))\) 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 5
10.8.a.a 10.a 1.a $1$ $3.124$ \(\Q\) None \(8\) \(28\) \(125\) \(104\) $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+28q^{3}+2^{6}q^{4}+5^{3}q^{5}+224q^{6}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(10)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)