Properties

Label 2075.1.c
Level $2075$
Weight $1$
Character orbit 2075.c
Rep. character $\chi_{2075}(1576,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $8$
Sturm bound $210$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 2075 = 5^{2} \cdot 83 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2075.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 83 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(210\)
Trace bound: \(17\)

Dimensions

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

Total New Old
Modular forms 20 14 6
Cusp forms 14 11 3
Eisenstein series 6 3 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 11 0 0 0

Trace form

\( 11 q + q^{3} + 5 q^{4} + q^{7} + 2 q^{9} + O(q^{10}) \) \( 11 q + q^{3} + 5 q^{4} + q^{7} + 2 q^{9} - 3 q^{11} + q^{12} + 7 q^{16} + q^{17} - 5 q^{21} - 2 q^{23} - 4 q^{26} - q^{27} + q^{28} + q^{29} - 3 q^{31} - q^{33} + 8 q^{36} + q^{37} - 6 q^{41} + 5 q^{44} + q^{48} + 2 q^{49} - 5 q^{51} + q^{59} - 3 q^{61} + 9 q^{64} + q^{68} - 2 q^{69} - q^{77} + 9 q^{81} - q^{83} - 5 q^{84} - 4 q^{86} - q^{87} - 2 q^{92} - q^{93} + 4 q^{94} - 4 q^{99} + O(q^{100}) \)

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.c.a 2075.c 83.b $1$ $1.036$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(-2\) \(0\) \(1\) \(q-2q^{3}+q^{4}+q^{7}+3q^{9}-q^{11}-2q^{12}+\cdots\)
2075.1.c.b 2075.c 83.b $1$ $1.036$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots\)
2075.1.c.c 2075.c 83.b $1$ $1.036$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(-1\) \(0\) \(2\) \(q-q^{3}+q^{4}+2q^{7}+2q^{11}-q^{12}+\cdots\)
2075.1.c.d 2075.c 83.b $1$ $1.036$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(1\) \(0\) \(-2\) \(q+q^{3}+q^{4}-2q^{7}+2q^{11}+q^{12}+\cdots\)
2075.1.c.e 2075.c 83.b $1$ $1.036$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(1\) \(0\) \(1\) \(q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}+q^{16}+\cdots\)
2075.1.c.f 2075.c 83.b $1$ $1.036$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(1\) \(0\) \(1\) \(q+q^{3}+q^{4}+q^{7}-q^{11}+q^{12}+q^{16}+\cdots\)
2075.1.c.g 2075.c 83.b $1$ $1.036$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-83}) \) None \(0\) \(2\) \(0\) \(-1\) \(q+2q^{3}+q^{4}-q^{7}+3q^{9}-q^{11}+2q^{12}+\cdots\)
2075.1.c.h 2075.c 83.b $4$ $1.036$ \(\Q(i, \sqrt{5})\) $D_{5}$ \(\Q(\sqrt{-415}) \) 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 \(S_{1}^{\mathrm{old}}(2075, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2075, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(83, [\chi])\)\(^{\oplus 3}\)