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Properties

Label 2600.1.o
Level $2600$
Weight $1$
Character orbit 2600.o
Rep. character $\chi_{2600}(51,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $6$
Sturm bound $420$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2600.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(420\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2600, [\chi])\).

Total New Old
Modular forms 26 14 12
Cusp forms 14 8 6
Eisenstein series 12 6 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 8 0 0 0

Trace form

\( 8 q + 2 q^{3} + 8 q^{4} + 6 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{3} + 8 q^{4} + 6 q^{9} + 2 q^{12} - 2 q^{14} + 8 q^{16} + 2 q^{17} - 4 q^{26} - 2 q^{27} + 6 q^{36} - 2 q^{42} + 2 q^{43} + 2 q^{48} + 6 q^{49} - 10 q^{51} - 2 q^{56} - 4 q^{62} + 8 q^{64} + 2 q^{68} - 2 q^{74} + 2 q^{78} + 4 q^{81} - 2 q^{91} - 2 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2600.1.o.a 2600.o 104.h $1$ $1.298$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-26}) \) \(\Q(\sqrt{65}) \) \(-1\) \(0\) \(0\) \(-2\) \(q-q^{2}+q^{4}-2q^{7}-q^{8}-q^{9}+q^{13}+\cdots\)
2600.1.o.b 2600.o 104.h $1$ $1.298$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(-1\) \(1\) \(0\) \(1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
2600.1.o.c 2600.o 104.h $1$ $1.298$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-26}) \) \(\Q(\sqrt{65}) \) \(1\) \(0\) \(0\) \(2\) \(q+q^{2}+q^{4}+2q^{7}+q^{8}-q^{9}-q^{13}+\cdots\)
2600.1.o.d 2600.o 104.h $1$ $1.298$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-26}) \) None \(1\) \(1\) \(0\) \(-1\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
2600.1.o.e 2600.o 104.h $2$ $1.298$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-26}) \) None \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+q^{7}-q^{8}+\cdots\)
2600.1.o.f 2600.o 104.h $2$ $1.298$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-26}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}-q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2600, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2600, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 3}\)