Properties

Label 275.1.c
Level $275$
Weight $1$
Character orbit 275.c
Rep. character $\chi_{275}(76,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 275.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(275, [\chi])\).

Total New Old
Modular forms 7 4 3
Cusp forms 1 1 0
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 1 0 0 0

Trace form

\( q + q^{4} - q^{9} + O(q^{10}) \) \( q + q^{4} - q^{9} - q^{11} + q^{16} - 2 q^{31} - q^{36} - q^{44} + q^{49} - 2 q^{59} + q^{64} + 2 q^{71} + q^{81} + 2 q^{89} + q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(275, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
275.1.c.a $1$ $0.137$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-q^{9}-q^{11}+q^{16}-2q^{31}+\cdots\)