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Properties

Label 215.2.a
Level $215$
Weight $2$
Character orbit 215.a
Rep. character $\chi_{215}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $4$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(44\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(215))\).

Total New Old
Modular forms 24 15 9
Cusp forms 21 15 6
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)\(43\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(6\)
\(-\)\(+\)$-$\(8\)
Plus space\(+\)\(1\)
Minus space\(-\)\(14\)

Trace form

\( 15 q + 3 q^{2} + 4 q^{3} + 17 q^{4} + q^{5} - 4 q^{6} + 8 q^{7} + 3 q^{8} + 23 q^{9} + O(q^{10}) \) \( 15 q + 3 q^{2} + 4 q^{3} + 17 q^{4} + q^{5} - 4 q^{6} + 8 q^{7} + 3 q^{8} + 23 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 8 q^{13} - 8 q^{14} - 4 q^{15} + 33 q^{16} - 4 q^{17} - 9 q^{18} + 4 q^{19} + 7 q^{20} + 4 q^{22} - 6 q^{23} - 36 q^{24} + 15 q^{25} - 26 q^{26} - 8 q^{27} + 12 q^{28} + 2 q^{29} - 4 q^{30} + 22 q^{31} - 21 q^{32} + 8 q^{33} - 10 q^{34} - 4 q^{35} + 5 q^{36} + 34 q^{37} - 40 q^{38} - 24 q^{39} - 15 q^{40} + 16 q^{41} - 72 q^{42} - 3 q^{43} - 32 q^{44} + 13 q^{45} - 4 q^{46} - 28 q^{47} - 68 q^{48} + 35 q^{49} + 3 q^{50} - 32 q^{51} - 34 q^{52} - 24 q^{53} - 74 q^{54} + 4 q^{55} - 30 q^{56} + 20 q^{57} + 2 q^{58} + 4 q^{59} - 14 q^{60} - 2 q^{61} - 20 q^{62} + 12 q^{63} + 17 q^{64} - 2 q^{65} - 14 q^{66} + 34 q^{67} + 14 q^{68} - 20 q^{69} + 12 q^{71} + 3 q^{72} + 34 q^{73} + 44 q^{74} + 4 q^{75} + 20 q^{76} - 28 q^{77} + 60 q^{78} + 8 q^{79} + 15 q^{80} + 87 q^{81} + 38 q^{82} - 42 q^{83} + 10 q^{84} - 10 q^{85} + 3 q^{86} - 24 q^{87} + 56 q^{88} + 22 q^{89} + 13 q^{90} - 4 q^{92} - 12 q^{93} - 36 q^{94} - 4 q^{95} + 14 q^{96} + 60 q^{97} + 39 q^{98} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(215))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 43
215.2.a.a 215.a 1.a $1$ $1.717$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}-2q^{7}-3q^{9}-q^{11}+\cdots\)
215.2.a.b 215.a 1.a $3$ $1.717$ 3.3.321.1 None \(-2\) \(1\) \(3\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
215.2.a.c 215.a 1.a $5$ $1.717$ 5.5.1933097.1 None \(2\) \(-1\) \(5\) \(5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots\)
215.2.a.d 215.a 1.a $6$ $1.717$ 6.6.32503921.1 None \(3\) \(4\) \(-6\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(215))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(215)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 2}\)