Properties

Label 1575.1.h
Level $1575$
Weight $1$
Character orbit 1575.h
Rep. character $\chi_{1575}(1126,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $5$
Sturm bound $240$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1575.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(240\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1575, [\chi])\).

Total New Old
Modular forms 40 10 30
Cusp forms 16 7 9
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 7 0 0 0

Trace form

\( 7 q + 7 q^{4} + q^{7} + O(q^{10}) \) \( 7 q + 7 q^{4} + q^{7} + 2 q^{11} + 2 q^{14} + 3 q^{16} - q^{28} + 2 q^{29} + 2 q^{37} + 2 q^{43} - 10 q^{46} + 7 q^{49} - 2 q^{56} - 3 q^{64} - 2 q^{67} + 2 q^{71} - 2 q^{74} - 4 q^{79} - 2 q^{86} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1575.1.h.a $1$ $0.786$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q-q^{2}-q^{7}+q^{8}+q^{11}+q^{14}-q^{16}+\cdots\)
1575.1.h.b $1$ $0.786$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{21}) \) \(0\) \(0\) \(0\) \(1\) \(q-q^{4}+q^{7}+q^{16}-q^{28}+2q^{37}+\cdots\)
1575.1.h.c $1$ $0.786$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(1\) \(q+q^{2}+q^{7}-q^{8}+q^{11}+q^{14}-q^{16}+\cdots\)
1575.1.h.d $2$ $0.786$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{2}+2q^{4}-q^{7}-\beta q^{8}-\beta q^{11}+\cdots\)
1575.1.h.e $2$ $0.786$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\beta q^{2}+2q^{4}+q^{7}-\beta q^{8}+\beta q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)