Properties

Label 1975.1.c
Level $1975$
Weight $1$
Character orbit 1975.c
Rep. character $\chi_{1975}(1974,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $200$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1975 = 5^{2} \cdot 79 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1975.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 395 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(200\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1975, [\chi])\).

Total New Old
Modular forms 24 6 18
Cusp forms 18 4 14
Eisenstein series 6 2 4

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q - 2 q^{4} - 4 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{4} - 4 q^{9} - 2 q^{11} + 2 q^{19} + 6 q^{26} - 2 q^{31} + 2 q^{36} + 6 q^{44} - 4 q^{46} - 4 q^{49} + 2 q^{64} + 4 q^{76} - 4 q^{79} + 4 q^{81} + 2 q^{89} + 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1975, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1975.1.c.a 1975.c 395.c $4$ $0.986$ \(\Q(i, \sqrt{5})\) $D_{5}$ \(\Q(\sqrt{-79}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{8}-q^{9}+\beta _{2}q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1975, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1975, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(395, [\chi])\)\(^{\oplus 2}\)