Properties

Label 10.4.a
Level $10$
Weight $4$
Character orbit 10.a
Rep. character $\chi_{10}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 10.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(10))\).

Total New Old
Modular forms 7 1 6
Cusp forms 3 1 2
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

\( q + 2 q^{2} - 8 q^{3} + 4 q^{4} + 5 q^{5} - 16 q^{6} - 4 q^{7} + 8 q^{8} + 37 q^{9} + O(q^{10}) \) \( q + 2 q^{2} - 8 q^{3} + 4 q^{4} + 5 q^{5} - 16 q^{6} - 4 q^{7} + 8 q^{8} + 37 q^{9} + 10 q^{10} + 12 q^{11} - 32 q^{12} - 58 q^{13} - 8 q^{14} - 40 q^{15} + 16 q^{16} + 66 q^{17} + 74 q^{18} - 100 q^{19} + 20 q^{20} + 32 q^{21} + 24 q^{22} + 132 q^{23} - 64 q^{24} + 25 q^{25} - 116 q^{26} - 80 q^{27} - 16 q^{28} - 90 q^{29} - 80 q^{30} + 152 q^{31} + 32 q^{32} - 96 q^{33} + 132 q^{34} - 20 q^{35} + 148 q^{36} - 34 q^{37} - 200 q^{38} + 464 q^{39} + 40 q^{40} - 438 q^{41} + 64 q^{42} + 32 q^{43} + 48 q^{44} + 185 q^{45} + 264 q^{46} - 204 q^{47} - 128 q^{48} - 327 q^{49} + 50 q^{50} - 528 q^{51} - 232 q^{52} + 222 q^{53} - 160 q^{54} + 60 q^{55} - 32 q^{56} + 800 q^{57} - 180 q^{58} + 420 q^{59} - 160 q^{60} + 902 q^{61} + 304 q^{62} - 148 q^{63} + 64 q^{64} - 290 q^{65} - 192 q^{66} - 1024 q^{67} + 264 q^{68} - 1056 q^{69} - 40 q^{70} + 432 q^{71} + 296 q^{72} + 362 q^{73} - 68 q^{74} - 200 q^{75} - 400 q^{76} - 48 q^{77} + 928 q^{78} - 160 q^{79} + 80 q^{80} - 359 q^{81} - 876 q^{82} + 72 q^{83} + 128 q^{84} + 330 q^{85} + 64 q^{86} + 720 q^{87} + 96 q^{88} + 810 q^{89} + 370 q^{90} + 232 q^{91} + 528 q^{92} - 1216 q^{93} - 408 q^{94} - 500 q^{95} - 256 q^{96} + 1106 q^{97} - 654 q^{98} + 444 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(10))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
10.4.a.a \(1\) \(0.590\) \(\Q\) None \(2\) \(-8\) \(5\) \(-4\) \(-\) \(-\) \(q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(10)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)