Properties

Label 25.6.a
Level $25$
Weight $6$
Character orbit 25.a
Rep. character $\chi_{25}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $4$
Sturm bound $15$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 25.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(15\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(25))\).

Total New Old
Modular forms 15 10 5
Cusp forms 9 7 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.
\(+\)\(3\)
\(-\)\(4\)

Trace form

\( 7q - 2q^{2} + 4q^{3} + 134q^{4} - 126q^{6} - 192q^{7} + 120q^{8} + 471q^{9} + O(q^{10}) \) \( 7q - 2q^{2} + 4q^{3} + 134q^{4} - 126q^{6} - 192q^{7} + 120q^{8} + 471q^{9} - 36q^{11} - 112q^{12} - 286q^{13} - 372q^{14} + 402q^{16} + 1678q^{17} + 454q^{18} - 4860q^{19} + 2784q^{21} + 296q^{22} - 2976q^{23} + 270q^{24} - 7356q^{26} - 1880q^{27} + 5376q^{28} + 2610q^{29} + 8864q^{31} - 5152q^{32} - 592q^{33} + 27718q^{34} - 24648q^{36} - 182q^{37} - 2120q^{38} + 11832q^{39} + 45714q^{41} + 1536q^{42} + 1244q^{43} - 63582q^{44} - 21436q^{46} + 12088q^{47} + 2624q^{48} - 29801q^{49} - 56496q^{51} + 8008q^{52} - 23846q^{53} - 12810q^{54} + 101340q^{56} + 4240q^{57} + 6820q^{58} + 53220q^{59} - 27886q^{61} + 4896q^{62} + 43584q^{63} + 102594q^{64} + 44898q^{66} - 60972q^{67} - 46984q^{68} - 71808q^{69} - 100536q^{71} - 27240q^{72} + 38774q^{73} + 103248q^{74} - 159470q^{76} + 28416q^{77} + 2288q^{78} - 6240q^{79} - 5433q^{81} + 18796q^{82} - 16716q^{83} - 91692q^{84} + 500904q^{86} - 13640q^{87} - 17760q^{88} - 24270q^{89} - 496q^{91} + 83328q^{92} - 9792q^{93} - 407312q^{94} - 341826q^{96} + 119038q^{97} - 40114q^{98} + 554292q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(25))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
25.6.a.a \(1\) \(4.010\) \(\Q\) None \(-2\) \(4\) \(0\) \(-192\) \(+\) \(q-2q^{2}+4q^{3}-28q^{4}-8q^{6}-192q^{7}+\cdots\)
25.6.a.b \(2\) \(4.010\) \(\Q(\sqrt{241}) \) None \(-5\) \(-20\) \(0\) \(-200\) \(+\) \(q+(-2-\beta )q^{2}+(-11+2\beta )q^{3}+(2^{5}+\cdots)q^{4}+\cdots\)
25.6.a.c \(2\) \(4.010\) \(\Q(\sqrt{11}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(q+\beta q^{2}+3\beta q^{3}+12q^{4}+132q^{6}+\cdots\)
25.6.a.d \(2\) \(4.010\) \(\Q(\sqrt{241}) \) None \(5\) \(20\) \(0\) \(200\) \(-\) \(q+(3-\beta )q^{2}+(9+2\beta )q^{3}+(37-5\beta )q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)