Properties

Label 2075.1.d
Level $2075$
Weight $1$
Character orbit 2075.d
Rep. character $\chi_{2075}(2074,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $4$
Sturm bound $210$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 2075 = 5^{2} \cdot 83 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2075.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 415 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(210\)
Trace bound: \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2075, [\chi])\).

Total New Old
Modular forms 22 10 12
Cusp forms 16 8 8
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 8 0 0 0

Trace form

\( 8 q - 8 q^{4} - 6 q^{9} + O(q^{10}) \) \( 8 q - 8 q^{4} - 6 q^{9} - 2 q^{11} + 8 q^{16} - 4 q^{21} + 2 q^{29} - 2 q^{31} + 6 q^{36} - 2 q^{41} + 2 q^{44} - 6 q^{49} - 4 q^{51} + 2 q^{59} - 2 q^{61} - 8 q^{64} + 4 q^{69} + 4 q^{81} + 4 q^{84} + 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2075, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2075.1.d.a 2075.d 415.d $2$ $1.036$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{4}-iq^{7}-3q^{9}-q^{11}+\cdots\)
2075.1.d.b 2075.d 415.d $2$ $1.036$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{4}+iq^{7}-q^{11}+iq^{12}+\cdots\)
2075.1.d.c 2075.d 415.d $2$ $1.036$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-q^{4}-iq^{7}-q^{11}-iq^{12}+\cdots\)
2075.1.d.d 2075.d 415.d $2$ $1.036$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-q^{4}-iq^{7}+q^{11}+iq^{12}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2075, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2075, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(415, [\chi])\)\(^{\oplus 2}\)