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Properties

Label 2775.1.h
Level $2775$
Weight $1$
Character orbit 2775.h
Rep. character $\chi_{2775}(776,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $4$
Sturm bound $380$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2775 = 3 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2775.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 111 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(380\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2775, [\chi])\).

Total New Old
Modular forms 32 17 15
Cusp forms 20 11 9
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 11 0 0 0

Trace form

\( 11 q + q^{3} + 9 q^{4} + 2 q^{7} + 11 q^{9} + O(q^{10}) \) \( 11 q + q^{3} + 9 q^{4} + 2 q^{7} + 11 q^{9} + 3 q^{12} + 7 q^{16} - 2 q^{21} + q^{27} - 2 q^{28} - 12 q^{34} + 9 q^{36} + q^{37} - 4 q^{46} - 3 q^{48} + 9 q^{49} - 4 q^{58} + 2 q^{63} + 5 q^{64} + 2 q^{67} + 2 q^{73} + 11 q^{81} - 14 q^{84} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2775, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2775.1.h.a 2775.h 111.d $1$ $1.385$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-111}) \) \(\Q(\sqrt{37}) \) \(0\) \(-1\) \(0\) \(2\) \(q-q^{3}-q^{4}+2q^{7}+q^{9}+q^{12}+q^{16}+\cdots\)
2775.1.h.b 2775.h 111.d $2$ $1.385$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-111}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}+q^{12}+\cdots\)
2775.1.h.c 2775.h 111.d $4$ $1.385$ \(\Q(\zeta_{16})^+\) $D_{8}$ \(\Q(\sqrt{-111}) \) None \(0\) \(-4\) \(0\) \(0\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2775.1.h.d 2775.h 111.d $4$ $1.385$ \(\Q(\zeta_{16})^+\) $D_{8}$ \(\Q(\sqrt{-111}) \) None \(0\) \(4\) \(0\) \(0\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2775, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2775, [\chi]) \cong \)