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Properties

Label 2500.1.h
Level $2500$
Weight $1$
Character orbit 2500.h
Rep. character $\chi_{2500}(499,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $24$
Newform subspaces $5$
Sturm bound $375$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2500 = 2^{2} \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2500.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 5 \)
Sturm bound: \(375\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2500, [\chi])\).

Total New Old
Modular forms 160 72 88
Cusp forms 40 24 16
Eisenstein series 120 48 72

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 24 0 0 0

Trace form

\( 24 q - 2 q^{4} + 2 q^{6} + O(q^{10}) \) \( 24 q - 2 q^{4} + 2 q^{6} + 2 q^{14} - 6 q^{16} + 4 q^{21} - 8 q^{24} - 4 q^{26} - 4 q^{29} + 4 q^{34} - 4 q^{36} + 8 q^{41} + 2 q^{46} + 4 q^{54} + 2 q^{56} + 8 q^{61} - 2 q^{64} + 4 q^{69} + 4 q^{74} - 2 q^{81} + 4 q^{84} + 2 q^{86} + 6 q^{89} + 2 q^{94} + 2 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2500, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2500.1.h.a 2500.h 100.h $4$ $1.248$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-5}) \) None \(-1\) \(-2\) \(0\) \(-2\) \(q+\zeta_{10}^{4}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
2500.1.h.b 2500.h 100.h $4$ $1.248$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-5}) \) None \(-1\) \(3\) \(0\) \(-2\) \(q+\zeta_{10}^{4}q^{2}+(1-\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
2500.1.h.c 2500.h 100.h $4$ $1.248$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-5}) \) None \(1\) \(-3\) \(0\) \(2\) \(q-\zeta_{10}^{4}q^{2}+(-1+\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
2500.1.h.d 2500.h 100.h $4$ $1.248$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-5}) \) None \(1\) \(2\) \(0\) \(2\) \(q-\zeta_{10}^{4}q^{2}+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{3}+\cdots\)
2500.1.h.e 2500.h 100.h $8$ $1.248$ \(\Q(\zeta_{20})\) $D_{5}$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{3}q^{2}+\zeta_{20}^{6}q^{4}+\zeta_{20}^{9}q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2500, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2500, [\chi]) \cong \)