Properties

Label 2475.1.b
Level $2475$
Weight $1$
Character orbit 2475.b
Rep. character $\chi_{2475}(901,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $3$
Sturm bound $360$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2475.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(360\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2475, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 8 5 3
Eisenstein series 24 3 21

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2475.1.b.a $1$ $1.235$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{11}+q^{16}-2q^{31}+q^{44}+\cdots\)
2475.1.b.b $2$ $1.235$ \(\Q(\sqrt{-2}) \) $D_{4}$ \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-q^{4}-\beta q^{7}-q^{11}-\beta q^{13}+\cdots\)
2475.1.b.c $2$ $1.235$ \(\Q(\sqrt{-2}) \) $D_{4}$ \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-q^{4}-\beta q^{7}+q^{11}-\beta q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)