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Properties

Label 495.1.h
Level $495$
Weight $1$
Character orbit 495.h
Rep. character $\chi_{495}(109,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $3$
Sturm bound $72$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 495.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(495, [\chi])\).

Total New Old
Modular forms 16 7 9
Cusp forms 8 5 3
Eisenstein series 8 2 6

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 5 0 0 0

Trace form

\( 5 q + 3 q^{4} + q^{5} + O(q^{10}) \) \( 5 q + 3 q^{4} + q^{5} + q^{11} - 3 q^{16} - q^{20} + 5 q^{25} - 2 q^{31} - 8 q^{34} - q^{44} + 3 q^{49} - 3 q^{55} - 2 q^{59} - 5 q^{64} - 8 q^{70} - 2 q^{71} + q^{80} + 2 q^{89} - 8 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(495, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
495.1.h.a 495.h 55.d $1$ $0.247$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q-q^{4}+q^{5}+q^{11}+q^{16}-q^{20}+q^{25}+\cdots\)
495.1.h.b 495.h 55.d $2$ $0.247$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{2}+q^{4}-q^{5}-\beta q^{7}+\beta q^{10}+\cdots\)
495.1.h.c 495.h 55.d $2$ $0.247$ \(\Q(\sqrt{2}) \) $D_{4}$ \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta q^{2}+q^{4}+q^{5}+\beta q^{7}-\beta q^{10}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(495, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(495, [\chi]) \cong \)