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Properties

Label 275.2.h
Level $275$
Weight $2$
Character orbit 275.h
Rep. character $\chi_{275}(26,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $64$
Newform subspaces $5$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(275, [\chi])\).

Total New Old
Modular forms 144 88 56
Cusp forms 96 64 32
Eisenstein series 48 24 24

Trace form

\( 64 q + 6 q^{2} + 4 q^{3} - 8 q^{4} - 18 q^{6} + 4 q^{7} - 2 q^{8} + 4 q^{9} + O(q^{10}) \) \( 64 q + 6 q^{2} + 4 q^{3} - 8 q^{4} - 18 q^{6} + 4 q^{7} - 2 q^{8} + 4 q^{9} - 18 q^{11} + 12 q^{12} - 2 q^{13} + 18 q^{14} - 8 q^{16} + 12 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{21} - 26 q^{22} + 8 q^{23} - 54 q^{24} - 32 q^{26} - 20 q^{27} + 2 q^{28} - 14 q^{29} - 16 q^{31} - 28 q^{32} + 14 q^{33} + 40 q^{34} + 22 q^{36} - 28 q^{37} + 6 q^{38} + 6 q^{39} + 2 q^{41} - 38 q^{42} - 4 q^{43} - 46 q^{44} - 20 q^{46} - 4 q^{47} + 14 q^{48} + 28 q^{49} + 42 q^{51} + 54 q^{52} - 16 q^{53} + 136 q^{54} - 8 q^{56} + 50 q^{57} - 6 q^{58} - 20 q^{59} - 4 q^{61} + 68 q^{62} - 26 q^{63} + 68 q^{64} - 26 q^{66} + 40 q^{67} - 46 q^{68} + 22 q^{69} - 36 q^{71} + 64 q^{72} + 10 q^{73} + 6 q^{74} - 52 q^{76} - 6 q^{77} + 4 q^{78} - 62 q^{79} - 10 q^{81} - 30 q^{82} - 2 q^{83} - 96 q^{84} - 8 q^{86} - 68 q^{87} + 14 q^{88} - 84 q^{89} - 56 q^{91} - 92 q^{92} + 48 q^{93} - 44 q^{94} + 136 q^{96} - 36 q^{97} + 68 q^{98} + 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(275, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
275.2.h.a 275.h 11.c $8$ $2.196$ 8.0.13140625.1 None \(2\) \(5\) \(0\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{6}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
275.2.h.b 275.h 11.c $8$ $2.196$ 8.0.159390625.1 None \(4\) \(-1\) \(0\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
275.2.h.c 275.h 11.c $16$ $2.196$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{14}q^{3}+(-1+\cdots)q^{4}+\cdots\)
275.2.h.d 275.h 11.c $16$ $2.196$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}+\beta _{12}+\beta _{13})q^{2}+(-\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots\)
275.2.h.e 275.h 11.c $16$ $2.196$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{2}-\beta _{5}+\beta _{9})q^{2}+\beta _{14}q^{3}+(-1+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(275, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)