Properties

Label 25.4.a
Level $25$
Weight $4$
Character orbit 25.a
Rep. character $\chi_{25}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $10$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 25.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(10\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(25))\).

Total New Old
Modular forms 11 6 5
Cusp forms 5 3 2
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
\(+\)\(2\)
\(-\)\(1\)

Trace form

\( 3 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{6} - 6 q^{7} + 21 q^{9} - 54 q^{11} - 16 q^{12} + 38 q^{13} - 12 q^{14} + 18 q^{16} - 26 q^{17} - 92 q^{18} + 30 q^{19} + 96 q^{21} + 128 q^{22} + 78 q^{23} - 210 q^{24}+ \cdots - 2628 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(25))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
25.4.a.a 25.a 1.a $1$ $1.475$ \(\Q\) None 25.4.a.a \(-1\) \(-7\) \(0\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-7q^{3}-7q^{4}+7q^{6}-6q^{7}+\cdots\)
25.4.a.b 25.a 1.a $1$ $1.475$ \(\Q\) None 25.4.a.a \(1\) \(7\) \(0\) \(6\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+7q^{3}-7q^{4}+7q^{6}+6q^{7}+\cdots\)
25.4.a.c 25.a 1.a $1$ $1.475$ \(\Q\) None 5.4.a.a \(4\) \(-2\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-2q^{3}+8q^{4}-8q^{6}-6q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(25)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)