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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1815.2.c.a 1815.c 5.b $2$ $14.493$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}+(-1-2i)q^{5}+\cdots\)
1815.2.c.b 1815.c 5.b $2$ $14.493$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots\)
1815.2.c.c 1815.c 5.b $4$ $14.493$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-3q^{4}+(-1-2\beta _{1}+\cdots)q^{5}+\cdots\)
1815.2.c.d 1815.c 5.b $6$ $14.493$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
1815.2.c.e 1815.c 5.b $6$ $14.493$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1815.2.c.f 1815.c 5.b $8$ $14.493$ 8.0.49787136.1 None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}-\beta _{3}q^{3}+\beta _{4}q^{4}+(2-\beta _{3}+\cdots)q^{5}+\cdots\)
1815.2.c.g 1815.c 5.b $8$ $14.493$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+\zeta_{24}^{3}q^{3}+(-1+\cdots)q^{5}+\cdots\)
1815.2.c.h 1815.c 5.b $12$ $14.493$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
1815.2.c.i 1815.c 5.b $12$ $14.493$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-2+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
1815.2.c.j 1815.c 5.b $24$ $14.493$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1815.2.c.k 1815.c 5.b $24$ $14.493$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

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