Properties

Label 15.11.c
Level $15$
Weight $11$
Character orbit 15.c
Rep. character $\chi_{15}(11,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $1$
Sturm bound $22$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 15.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(15, [\chi])\).

Total New Old
Modular forms 22 14 8
Cusp forms 18 14 4
Eisenstein series 4 0 4

Trace form

\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21}+ \cdots + 36258312560 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{11}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.11.c.a 15.c 3.b $14$ $9.530$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 15.11.c.a \(0\) \(44\) \(0\) \(-50548\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(3+\beta _{2}-\beta _{3})q^{3}+(-629+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(15, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(15, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)