Properties

Label 2151.1.d
Level $2151$
Weight $1$
Character orbit 2151.d
Rep. character $\chi_{2151}(955,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $5$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2151.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 239 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(240\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2151, [\chi])\).

Total New Old
Modular forms 36 12 24
Cusp forms 32 11 21
Eisenstein series 4 1 3

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 7 0 4 0

Trace form

\( 11q + q^{2} + 6q^{4} + q^{5} + 2q^{8} + O(q^{10}) \) \( 11q + q^{2} + 6q^{4} + q^{5} + 2q^{8} - 6q^{10} + q^{11} + q^{16} + q^{17} + 3q^{20} - 6q^{22} + 6q^{25} + q^{29} - 5q^{31} + 3q^{32} - 6q^{34} + 3q^{44} + 3q^{49} + 3q^{50} + 2q^{55} - 6q^{58} + 3q^{61} - 13q^{62} + 8q^{64} - 5q^{67} + 3q^{68} + q^{71} - 10q^{80} + q^{83} + 2q^{85} + 8q^{91} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2151, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2151.1.d.a \(1\) \(1.073\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-239}) \) None \(1\) \(0\) \(1\) \(0\) \(q+q^{2}+q^{5}-q^{8}+q^{10}+q^{11}-q^{16}+\cdots\)
2151.1.d.b \(2\) \(1.073\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(-2\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{5}-\beta q^{7}+q^{8}-q^{10}+q^{11}+\cdots\)
2151.1.d.c \(2\) \(1.073\) \(\Q(\sqrt{5}) \) \(D_{5}\) \(\Q(\sqrt{-239}) \) None \(1\) \(0\) \(1\) \(0\) \(q+(1-\beta )q^{2}+(1-\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
2151.1.d.d \(2\) \(1.073\) \(\Q(\sqrt{-2}) \) \(S_{4}\) None None \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}-q^{5}-\beta q^{7}-q^{8}-q^{10}-q^{11}+\cdots\)
2151.1.d.e \(4\) \(1.073\) \(\Q(\zeta_{15})^+\) \(D_{15}\) \(\Q(\sqrt{-239}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2151, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2151, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(239, [\chi])\)\(^{\oplus 3}\)