Properties

Label 115.3.c
Level $115$
Weight $3$
Character orbit 115.c
Rep. character $\chi_{115}(114,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $3$
Sturm bound $36$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 115.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(36\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(115, [\chi])\).

Total New Old
Modular forms 26 26 0
Cusp forms 22 22 0
Eisenstein series 4 4 0

Trace form

\( 22 q - 48 q^{4} - 8 q^{6} - 54 q^{9} + O(q^{10}) \) \( 22 q - 48 q^{4} - 8 q^{6} - 54 q^{9} + 120 q^{16} + 44 q^{24} + 38 q^{25} - 56 q^{26} - 114 q^{29} + 130 q^{31} + 2 q^{35} + 40 q^{36} - 168 q^{39} + 58 q^{41} - 248 q^{46} + 152 q^{49} + 200 q^{50} - 196 q^{54} + 268 q^{55} + 62 q^{59} + 100 q^{64} + 376 q^{69} - 636 q^{70} - 142 q^{71} + 428 q^{75} - 826 q^{81} - 174 q^{85} + 276 q^{94} + 184 q^{95} - 264 q^{96} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(115, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.3.c.a 115.c 115.c $1$ $3.134$ \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(-5\) \(9\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}-5q^{5}+9q^{7}+9q^{9}+2^{4}q^{16}+\cdots\)
115.3.c.b 115.c 115.c $1$ $3.134$ \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(5\) \(-9\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}+5q^{5}-9q^{7}+9q^{9}+2^{4}q^{16}+\cdots\)
115.3.c.c 115.c 115.c $20$ $3.134$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-3+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots\)