Properties

Label 25.3.c
Level $25$
Weight $3$
Character orbit 25.c
Rep. character $\chi_{25}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 25.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(25, [\chi])\).

Total New Old
Modular forms 16 8 8
Cusp forms 4 4 0
Eisenstein series 12 4 8

Trace form

\( 4q - 12q^{6} + O(q^{10}) \) \( 4q - 12q^{6} - 12q^{11} + 44q^{16} + 48q^{21} - 72q^{26} - 152q^{31} + 24q^{36} + 228q^{41} + 168q^{46} - 132q^{51} - 240q^{56} - 112q^{61} + 36q^{66} + 168q^{71} + 20q^{76} - 36q^{81} + 48q^{86} + 288q^{91} + 108q^{96} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
25.3.c.a \(4\) \(0.681\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots\)