Properties

Label 1521.1.j
Level $1521$
Weight $1$
Character orbit 1521.j
Rep. character $\chi_{1521}(577,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $6$
Newform subspaces $3$
Sturm bound $182$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1521.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(182\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1521, [\chi])\).

Total New Old
Modular forms 66 16 50
Cusp forms 10 6 4
Eisenstein series 56 10 46

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6q + 2q^{7} + O(q^{10}) \) \( 6q + 2q^{7} + 2q^{16} + 2q^{19} + 8q^{22} - 2q^{28} - 2q^{31} - 2q^{37} - 8q^{55} + 2q^{67} + 2q^{73} + 2q^{76} + 8q^{94} - 2q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1521.1.j.a \(2\) \(0.759\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-39}) \) None \(-2\) \(0\) \(2\) \(0\) \(q+(-1-i)q^{2}+iq^{4}+(1+i)q^{5}-q^{8}+\cdots\)
1521.1.j.b \(2\) \(0.759\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{4}+(1-i)q^{7}-q^{16}+(1+i)q^{19}+\cdots\)
1521.1.j.c \(2\) \(0.759\) \(\Q(\sqrt{-1}) \) \(D_{4}\) \(\Q(\sqrt{-39}) \) None \(2\) \(0\) \(-2\) \(0\) \(q+(1+i)q^{2}+iq^{4}+(-1-i)q^{5}+q^{8}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)