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

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

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

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
25.6.a.a 25.a 1.a $1$ $4.010$ \(\Q\) None \(-2\) \(4\) \(0\) \(-192\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}-28q^{4}-8q^{6}-192q^{7}+\cdots\)
25.6.a.b 25.a 1.a $2$ $4.010$ \(\Q(\sqrt{241}) \) None \(-5\) \(-20\) \(0\) \(-200\) $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{2}+(-11+2\beta )q^{3}+(2^{5}+\cdots)q^{4}+\cdots\)
25.6.a.c 25.a 1.a $2$ $4.010$ \(\Q(\sqrt{11}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3\beta q^{3}+12q^{4}+132q^{6}+\cdots\)
25.6.a.d 25.a 1.a $2$ $4.010$ \(\Q(\sqrt{241}) \) None \(5\) \(20\) \(0\) \(200\) $-$ $\mathrm{SU}(2)$ \(q+(3-\beta )q^{2}+(9+2\beta )q^{3}+(37-5\beta )q^{4}+\cdots\)

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

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