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Properties

Label 25.4.a
Level $25$
Weight $4$
Character orbit 25.a
Rep. character $\chi_{25}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
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: \(\Q\)
Newform subspaces: \( 3 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.4.a.a 25.a 1.a $1$ $1.475$ \(\Q\) None \(-1\) \(-7\) \(0\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{3}-7q^{4}+7q^{6}-6q^{7}+\cdots\)
25.4.a.b 25.a 1.a $1$ $1.475$ \(\Q\) None \(1\) \(7\) \(0\) \(6\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+7q^{3}-7q^{4}+7q^{6}+6q^{7}+\cdots\)
25.4.a.c 25.a 1.a $1$ $1.475$ \(\Q\) None \(4\) \(-2\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-2q^{3}+8q^{4}-8q^{6}-6q^{7}+\cdots\)

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

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