Properties

Label 1815.2.c
Level $1815$
Weight $2$
Character orbit 1815.c
Rep. character $\chi_{1815}(364,\cdot)$
Character field $\Q$
Dimension $108$
Newform subspaces $11$
Sturm bound $528$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(528\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1815, [\chi])\).

Total New Old
Modular forms 288 108 180
Cusp forms 240 108 132
Eisenstein series 48 0 48

Trace form

\( 108q - 108q^{4} - 4q^{5} + 4q^{6} - 108q^{9} + O(q^{10}) \) \( 108q - 108q^{4} - 4q^{5} + 4q^{6} - 108q^{9} - 12q^{10} + 24q^{14} + 108q^{16} - 16q^{19} - 4q^{20} + 8q^{21} - 12q^{24} + 4q^{25} + 16q^{26} - 16q^{30} + 24q^{34} + 108q^{36} - 8q^{39} + 28q^{40} + 4q^{45} - 32q^{46} - 108q^{49} - 8q^{50} + 8q^{51} - 4q^{54} - 120q^{56} + 16q^{59} + 20q^{60} + 40q^{61} - 84q^{64} - 40q^{65} + 20q^{70} + 32q^{71} - 32q^{74} - 8q^{75} + 64q^{76} - 32q^{79} + 32q^{80} + 108q^{81} - 40q^{85} + 48q^{86} + 40q^{89} + 12q^{90} - 48q^{94} + 48q^{95} + 28q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1815.2.c.a \(2\) \(14.493\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}+(-1-2i)q^{5}+\cdots\)
1815.2.c.b \(2\) \(14.493\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots\)
1815.2.c.c \(4\) \(14.493\) \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-3q^{4}+(-1-2\beta _{1}+\cdots)q^{5}+\cdots\)
1815.2.c.d \(6\) \(14.493\) 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
1815.2.c.e \(6\) \(14.493\) 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{4}q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.2.c.f \(8\) \(14.493\) 8.0.49787136.1 None \(0\) \(0\) \(16\) \(0\) \(q+\beta _{6}q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+(2-\beta _{3}+\cdots)q^{5}+\cdots\)
1815.2.c.g \(8\) \(14.493\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+\zeta_{24}^{3}q^{3}+(-1+\cdots)q^{5}+\cdots\)
1815.2.c.h \(12\) \(14.493\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
1815.2.c.i \(12\) \(14.493\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
1815.2.c.j \(24\) \(14.493\) None \(0\) \(0\) \(-2\) \(0\)
1815.2.c.k \(24\) \(14.493\) None \(0\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1815, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)