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Properties

Label 215.2.b
Level $215$
Weight $2$
Character orbit 215.b
Rep. character $\chi_{215}(44,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $2$
Sturm bound $44$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 215 = 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 215.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(44\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(215, [\chi])\).

Total New Old
Modular forms 24 20 4
Cusp forms 20 20 0
Eisenstein series 4 0 4

Trace form

\( 20 q - 22 q^{4} - 4 q^{5} - 16 q^{9} + O(q^{10}) \) \( 20 q - 22 q^{4} - 4 q^{5} - 16 q^{9} - 6 q^{10} + 16 q^{14} + 8 q^{15} + 26 q^{16} - 12 q^{19} + 16 q^{20} - 16 q^{21} - 16 q^{24} + 4 q^{25} + 8 q^{26} - 8 q^{29} - 16 q^{30} - 24 q^{31} + 12 q^{34} + 24 q^{35} + 38 q^{36} - 4 q^{39} + 6 q^{40} - 20 q^{41} - 24 q^{44} + 16 q^{45} + 8 q^{46} - 8 q^{49} + 4 q^{50} + 36 q^{51} - 30 q^{54} + 8 q^{55} - 22 q^{56} + 24 q^{59} - 18 q^{60} - 12 q^{61} - 10 q^{64} + 8 q^{65} - 54 q^{66} + 24 q^{69} - 20 q^{70} + 8 q^{71} + 54 q^{74} - 12 q^{75} - 8 q^{76} + 24 q^{79} - 72 q^{80} - 52 q^{81} + 126 q^{84} + 32 q^{85} - 10 q^{86} - 20 q^{89} + 62 q^{90} - 16 q^{91} - 92 q^{94} + 26 q^{96} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(215, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
215.2.b.a 215.b 5.b $6$ $1.717$ 6.0.1827904.1 None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{4}-\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
215.2.b.b 215.b 5.b $14$ $1.717$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{9})q^{2}+(-\beta _{9}-\beta _{13})q^{3}+(-1+\cdots)q^{4}+\cdots\)