Properties

Label 25.4.a
Level 25
Weight 4
Character orbit a
Rep. character \(\chi_{25}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 10
Trace bound 2

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 25.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(10\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(25))\).

Total New Old
Modular forms 11 6 5
Cusp forms 5 3 2
Eisenstein series 6 3 3

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

\(5\)Dim.
\(+\)\(2\)
\(-\)\(1\)

Trace form

\(3q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 21q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 21q^{9} \) \(\mathstrut -\mathstrut 54q^{11} \) \(\mathstrut -\mathstrut 16q^{12} \) \(\mathstrut +\mathstrut 38q^{13} \) \(\mathstrut -\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 26q^{17} \) \(\mathstrut -\mathstrut 92q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut +\mathstrut 96q^{21} \) \(\mathstrut +\mathstrut 128q^{22} \) \(\mathstrut +\mathstrut 78q^{23} \) \(\mathstrut -\mathstrut 210q^{24} \) \(\mathstrut +\mathstrut 96q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut -\mathstrut 48q^{28} \) \(\mathstrut +\mathstrut 270q^{29} \) \(\mathstrut -\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 256q^{32} \) \(\mathstrut -\mathstrut 64q^{33} \) \(\mathstrut +\mathstrut 78q^{34} \) \(\mathstrut -\mathstrut 492q^{36} \) \(\mathstrut -\mathstrut 266q^{37} \) \(\mathstrut +\mathstrut 400q^{38} \) \(\mathstrut -\mathstrut 468q^{39} \) \(\mathstrut -\mathstrut 384q^{41} \) \(\mathstrut +\mathstrut 48q^{42} \) \(\mathstrut -\mathstrut 442q^{43} \) \(\mathstrut +\mathstrut 858q^{44} \) \(\mathstrut +\mathstrut 636q^{46} \) \(\mathstrut +\mathstrut 514q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut -\mathstrut 921q^{49} \) \(\mathstrut +\mathstrut 1326q^{51} \) \(\mathstrut +\mathstrut 304q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 330q^{54} \) \(\mathstrut -\mathstrut 180q^{56} \) \(\mathstrut -\mathstrut 200q^{57} \) \(\mathstrut -\mathstrut 200q^{58} \) \(\mathstrut -\mathstrut 60q^{59} \) \(\mathstrut -\mathstrut 1554q^{61} \) \(\mathstrut -\mathstrut 432q^{62} \) \(\mathstrut +\mathstrut 138q^{63} \) \(\mathstrut -\mathstrut 846q^{64} \) \(\mathstrut -\mathstrut 858q^{66} \) \(\mathstrut -\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 208q^{68} \) \(\mathstrut +\mathstrut 2112q^{69} \) \(\mathstrut +\mathstrut 1236q^{71} \) \(\mathstrut +\mathstrut 878q^{73} \) \(\mathstrut -\mathstrut 1692q^{74} \) \(\mathstrut +\mathstrut 1290q^{76} \) \(\mathstrut -\mathstrut 192q^{77} \) \(\mathstrut -\mathstrut 304q^{78} \) \(\mathstrut +\mathstrut 1620q^{79} \) \(\mathstrut -\mathstrut 1257q^{81} \) \(\mathstrut +\mathstrut 88q^{82} \) \(\mathstrut -\mathstrut 282q^{83} \) \(\mathstrut -\mathstrut 492q^{84} \) \(\mathstrut -\mathstrut 1584q^{86} \) \(\mathstrut +\mathstrut 100q^{87} \) \(\mathstrut -\mathstrut 2040q^{89} \) \(\mathstrut -\mathstrut 564q^{91} \) \(\mathstrut +\mathstrut 624q^{92} \) \(\mathstrut +\mathstrut 216q^{93} \) \(\mathstrut +\mathstrut 2448q^{94} \) \(\mathstrut +\mathstrut 2766q^{96} \) \(\mathstrut -\mathstrut 386q^{97} \) \(\mathstrut -\mathstrut 1228q^{98} \) \(\mathstrut -\mathstrut 2628q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(25))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
25.4.a.a \(1\) \(1.475\) \(\Q\) None \(-1\) \(-7\) \(0\) \(-6\) \(-\) \(q-q^{2}-7q^{3}-7q^{4}+7q^{6}-6q^{7}+\cdots\)
25.4.a.b \(1\) \(1.475\) \(\Q\) None \(1\) \(7\) \(0\) \(6\) \(+\) \(q+q^{2}+7q^{3}-7q^{4}+7q^{6}+6q^{7}+\cdots\)
25.4.a.c \(1\) \(1.475\) \(\Q\) None \(4\) \(-2\) \(0\) \(-6\) \(+\) \(q+4q^{2}-2q^{3}+8q^{4}-8q^{6}-6q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)