Properties

Label 10.10.a
Level 10
Weight 10
Character orbit a
Rep. character \(\chi_{10}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 3
Sturm bound 15
Trace bound 3

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 10.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(15\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 15 3 12
Cusp forms 11 3 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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3q - 16q^{2} + 16q^{3} + 768q^{4} - 625q^{5} + 5312q^{6} - 228q^{7} - 4096q^{8} + 14959q^{9} + O(q^{10}) \) \( 3q - 16q^{2} + 16q^{3} + 768q^{4} - 625q^{5} + 5312q^{6} - 228q^{7} - 4096q^{8} + 14959q^{9} - 10000q^{10} + 97356q^{11} + 4096q^{12} - 232974q^{13} + 152704q^{14} - 265000q^{15} + 196608q^{16} - 934458q^{17} + 99632q^{18} + 1372140q^{19} - 160000q^{20} - 772264q^{21} - 629952q^{22} + 2695956q^{23} + 1359872q^{24} + 1171875q^{25} - 1534688q^{26} - 3754160q^{27} - 58368q^{28} + 3847050q^{29} + 760000q^{30} - 4230024q^{31} - 1048576q^{32} - 10293648q^{33} - 4082976q^{34} + 6932500q^{35} + 3829504q^{36} + 28529802q^{37} - 31419200q^{38} - 3137392q^{39} - 2560000q^{40} - 2660874q^{41} + 38291968q^{42} - 39518424q^{43} + 24923136q^{44} + 18066875q^{45} + 38289792q^{46} - 27549708q^{47} + 1048576q^{48} + 36603891q^{49} - 6250000q^{50} - 129542784q^{51} - 59641344q^{52} + 181541706q^{53} + 9453440q^{54} + 31567500q^{55} + 39092224q^{56} - 239106400q^{57} - 180687840q^{58} + 32450100q^{59} - 67840000q^{60} - 108436254q^{61} + 142425088q^{62} + 349738556q^{63} + 50331648q^{64} + 2466250q^{65} + 326125824q^{66} - 56692488q^{67} - 239221248q^{68} + 49880328q^{69} - 204080000q^{70} + 26724816q^{71} + 25505792q^{72} + 283392846q^{73} - 109583456q^{74} + 6250000q^{75} + 351267840q^{76} + 594093984q^{77} - 865437056q^{78} - 1186742880q^{79} - 40960000q^{80} - 554831837q^{81} + 733577568q^{82} + 560234736q^{83} - 197699584q^{84} + 636138750q^{85} + 978928192q^{86} - 845703360q^{87} - 161267712q^{88} - 950284530q^{89} - 500930000q^{90} - 1862513064q^{91} + 690164736q^{92} + 2509309712q^{93} + 606303744q^{94} + 464237500q^{95} + 348127232q^{96} - 961141338q^{97} - 1182674832q^{98} + 2026475868q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(10))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
10.10.a.a \(1\) \(5.150\) \(\Q\) None \(-16\) \(-204\) \(625\) \(5432\) \(+\) \(-\) \(q-2^{4}q^{2}-204q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
10.10.a.b \(1\) \(5.150\) \(\Q\) None \(-16\) \(46\) \(-625\) \(-10318\) \(+\) \(+\) \(q-2^{4}q^{2}+46q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)
10.10.a.c \(1\) \(5.150\) \(\Q\) None \(16\) \(174\) \(-625\) \(4658\) \(-\) \(+\) \(q+2^{4}q^{2}+174q^{3}+2^{8}q^{4}-5^{4}q^{5}+\cdots\)

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

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