Properties

Label 25.6.b
Level $25$
Weight $6$
Character orbit 25.b
Rep. character $\chi_{25}(24,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $15$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 25.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(15\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(25, [\chi])\).

Total New Old
Modular forms 16 8 8
Cusp forms 10 6 4
Eisenstein series 6 2 4

Trace form

\( 6 q - 82 q^{4} - 398 q^{6} + 62 q^{9} + O(q^{10}) \) \( 6 q - 82 q^{4} - 398 q^{6} + 62 q^{9} - 688 q^{11} - 804 q^{14} + 3586 q^{16} + 4240 q^{19} + 4392 q^{21} - 6030 q^{24} - 8368 q^{26} + 14660 q^{29} - 7088 q^{31} - 33514 q^{34} - 21964 q^{36} - 5936 q^{39} + 36712 q^{41} + 65486 q^{44} + 16812 q^{46} - 16742 q^{49} - 22328 q^{51} - 14710 q^{54} + 62460 q^{56} + 16120 q^{59} + 15812 q^{61} - 65922 q^{64} - 20446 q^{66} - 13176 q^{69} - 239888 q^{71} + 81716 q^{74} - 194430 q^{76} - 64240 q^{79} + 187846 q^{81} + 41676 q^{84} + 492872 q^{86} - 57120 q^{89} + 68672 q^{91} + 291656 q^{94} - 197698 q^{96} - 510776 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.6.b.a $2$ $4.010$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}+28q^{4}-8q^{6}+96iq^{7}+\cdots\)
25.6.b.b $4$ $4.010$ \(\Q(i, \sqrt{241})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)