Properties

Label 115.3.d
Level $115$
Weight $3$
Character orbit 115.d
Rep. character $\chi_{115}(91,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 26 16 10
Cusp forms 22 16 6
Eisenstein series 4 0 4

Trace form

\( 16 q - 4 q^{2} + 16 q^{4} + 26 q^{6} + 22 q^{8} + 32 q^{9} + O(q^{10}) \) \( 16 q - 4 q^{2} + 16 q^{4} + 26 q^{6} + 22 q^{8} + 32 q^{9} - 30 q^{12} - 12 q^{13} - 8 q^{16} - 70 q^{18} + 34 q^{23} + 84 q^{24} - 80 q^{25} - 62 q^{26} + 96 q^{27} + 26 q^{29} + 10 q^{31} - 56 q^{32} - 50 q^{35} - 254 q^{36} - 76 q^{39} + 58 q^{41} + 96 q^{46} + 224 q^{47} - 226 q^{48} - 254 q^{49} + 20 q^{50} + 82 q^{52} - 26 q^{54} + 40 q^{55} + 174 q^{58} - 26 q^{59} - 130 q^{62} - 146 q^{64} + 280 q^{69} + 120 q^{70} + 18 q^{71} - 70 q^{72} + 168 q^{73} + 484 q^{77} - 106 q^{78} + 96 q^{81} - 2 q^{82} + 130 q^{85} - 44 q^{87} - 152 q^{92} - 76 q^{93} + 150 q^{94} + 80 q^{95} - 398 q^{96} + 692 q^{98} + O(q^{100}) \)

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.d.a 115.d 23.b $6$ $3.134$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{4}q^{3}-3q^{4}-\beta _{3}q^{5}-\beta _{4}q^{6}+\cdots\)
115.3.d.b 115.d 23.b $10$ $3.134$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{7}q^{3}+(3+\beta _{6})q^{4}+\beta _{5}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(115, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(115, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)