Properties

Label 25.3.c
Level 25
Weight 3
Character orbit c
Rep. character \(\chi_{25}(7,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 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: \(\Q(i)\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(25, [\chi])\) into irreducible Hecke orbits

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 \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots\)