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Properties

Label 25.8.a
Level $25$
Weight $8$
Character orbit 25.a
Rep. character $\chi_{25}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $5$
Sturm bound $20$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 25.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(20\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(25))\).

Total New Old
Modular forms 21 12 9
Cusp forms 15 9 6
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
\(+\)\(5\)
\(-\)\(4\)

Trace form

\( 9 q - 6 q^{2} + 28 q^{3} + 502 q^{4} + 858 q^{6} + 1744 q^{7} - 2280 q^{8} - 1167 q^{9} + O(q^{10}) \) \( 9 q - 6 q^{2} + 28 q^{3} + 502 q^{4} + 858 q^{6} + 1744 q^{7} - 2280 q^{8} - 1167 q^{9} - 252 q^{11} + 26624 q^{12} - 7402 q^{13} - 42036 q^{14} + 37394 q^{16} + 39594 q^{17} - 29582 q^{18} + 35500 q^{19} - 96072 q^{21} - 103832 q^{22} + 111168 q^{23} + 195150 q^{24} + 107868 q^{26} - 305720 q^{27} - 53648 q^{28} - 93450 q^{29} - 289392 q^{31} - 100896 q^{32} + 449216 q^{33} - 297866 q^{34} + 182424 q^{36} + 12894 q^{37} - 702120 q^{38} + 111336 q^{39} - 550962 q^{41} + 1649808 q^{42} + 75908 q^{43} - 37806 q^{44} + 2571428 q^{46} + 502344 q^{47} - 1964032 q^{48} + 1064737 q^{49} + 102168 q^{51} + 1415784 q^{52} + 3672078 q^{53} - 2464050 q^{54} - 5836500 q^{56} - 2021840 q^{57} - 3386980 q^{58} - 1200300 q^{59} + 5259198 q^{61} - 4839072 q^{62} + 1831968 q^{63} - 1223518 q^{64} - 3252774 q^{66} - 3719156 q^{67} + 5744952 q^{68} + 10103256 q^{69} - 4694472 q^{71} - 1178760 q^{72} - 301582 q^{73} + 12747624 q^{74} + 13388450 q^{76} - 2894832 q^{77} - 7266064 q^{78} - 7920800 q^{79} - 9219471 q^{81} + 12540308 q^{82} + 3652188 q^{83} - 29593116 q^{84} + 3975048 q^{86} + 20541640 q^{87} - 10712160 q^{88} - 15233850 q^{89} - 8590112 q^{91} + 6316944 q^{92} - 14003664 q^{93} + 29492944 q^{94} + 17782878 q^{96} + 272394 q^{97} + 38814042 q^{98} - 4347324 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(25))\) 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
25.8.a.a 25.a 1.a $1$ $7.810$ \(\Q\) None \(14\) \(48\) \(0\) \(1644\) $+$ $\mathrm{SU}(2)$ \(q+14q^{2}+48q^{3}+68q^{4}+672q^{6}+\cdots\)
25.8.a.b 25.a 1.a $2$ $7.810$ \(\Q(\sqrt{19}) \) None \(-20\) \(-20\) \(0\) \(100\) $+$ $\mathrm{SU}(2)$ \(q+(-10+\beta )q^{2}+(-10-8\beta )q^{3}+(48+\cdots)q^{4}+\cdots\)
25.8.a.c 25.a 1.a $2$ $7.810$ \(\Q(\sqrt{649}) \) None \(-15\) \(-40\) \(0\) \(600\) $-$ $\mathrm{SU}(2)$ \(q+(-7-\beta )q^{2}+(-19-2\beta )q^{3}+(83+\cdots)q^{4}+\cdots\)
25.8.a.d 25.a 1.a $2$ $7.810$ \(\Q(\sqrt{29}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3\beta q^{3}-12q^{4}-348q^{6}+\cdots\)
25.8.a.e 25.a 1.a $2$ $7.810$ \(\Q(\sqrt{649}) \) None \(15\) \(40\) \(0\) \(-600\) $+$ $\mathrm{SU}(2)$ \(q+(8-\beta )q^{2}+(21-2\beta )q^{3}+(98-15\beta )q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)