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Properties

Label 355.2.a
Level $355$
Weight $2$
Character orbit 355.a
Rep. character $\chi_{355}(1,\cdot)$
Character field $\Q$
Dimension $23$
Newform subspaces $5$
Sturm bound $72$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 355 = 5 \cdot 71 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 355.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(72\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(355))\).

Total New Old
Modular forms 38 23 15
Cusp forms 35 23 12
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.

\(5\)\(71\)FrickeDim
\(+\)\(+\)$+$\(4\)
\(+\)\(-\)$-$\(8\)
\(-\)\(+\)$-$\(7\)
\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(8\)
Minus space\(-\)\(15\)

Trace form

\( 23 q + q^{2} - 4 q^{3} + 21 q^{4} - q^{5} - 4 q^{7} + 9 q^{8} + 15 q^{9} + O(q^{10}) \) \( 23 q + q^{2} - 4 q^{3} + 21 q^{4} - q^{5} - 4 q^{7} + 9 q^{8} + 15 q^{9} - 3 q^{10} + 4 q^{12} - 10 q^{13} + 16 q^{14} + 29 q^{16} + 2 q^{17} + 29 q^{18} - 16 q^{19} + q^{20} - 12 q^{21} + 8 q^{23} - 16 q^{24} + 23 q^{25} + 2 q^{26} - 16 q^{27} - 28 q^{28} + 6 q^{29} - 12 q^{30} - 12 q^{31} + 29 q^{32} - 16 q^{33} - 10 q^{34} + 4 q^{35} - 19 q^{36} + 6 q^{37} - 24 q^{38} - 4 q^{39} - 15 q^{40} - 26 q^{41} - 36 q^{42} - 8 q^{43} - 16 q^{44} - 5 q^{45} - 12 q^{47} - 16 q^{48} + 3 q^{49} + q^{50} + 44 q^{51} + 2 q^{52} + 34 q^{53} - 40 q^{54} + 4 q^{55} - 20 q^{56} - 20 q^{57} + 42 q^{58} + 20 q^{59} - 12 q^{60} - 14 q^{61} + 8 q^{62} + 24 q^{63} + 57 q^{64} + 2 q^{65} - 24 q^{66} - 4 q^{67} - 18 q^{68} + 44 q^{69} + 12 q^{70} + q^{71} + 13 q^{72} - 50 q^{73} - 22 q^{74} - 4 q^{75} - 52 q^{76} + 44 q^{77} - 76 q^{78} + 20 q^{79} + q^{80} - 9 q^{81} - 26 q^{82} + 32 q^{83} - 80 q^{84} + 2 q^{85} + 4 q^{86} + 16 q^{87} + 8 q^{88} + 10 q^{89} + 13 q^{90} - 28 q^{91} - 28 q^{92} + 28 q^{93} - 20 q^{94} - 48 q^{96} - 18 q^{97} + 9 q^{98} - 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(355))\) 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 71
355.2.a.a 355.a 1.a $1$ $2.835$ \(\Q\) None \(0\) \(-2\) \(1\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+q^{5}-q^{7}+q^{9}+4q^{12}+\cdots\)
355.2.a.b 355.a 1.a $4$ $2.835$ 4.4.1957.1 None \(-4\) \(-3\) \(4\) \(-5\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
355.2.a.c 355.a 1.a $4$ $2.835$ 4.4.725.1 None \(-2\) \(-1\) \(-4\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(\beta _{2}-\beta _{3})q^{4}-q^{5}+\cdots\)
355.2.a.d 355.a 1.a $6$ $2.835$ 6.6.62581037.1 None \(3\) \(3\) \(6\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
355.2.a.e 355.a 1.a $8$ $2.835$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(-1\) \(-8\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{4})q^{2}-\beta _{6}q^{3}+(1+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(355))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(355)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(71))\)\(^{\oplus 2}\)