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

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

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

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