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Properties

Label 275.2.k
Level $275$
Weight $2$
Character orbit 275.k
Rep. character $\chi_{275}(36,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $112$
Newform subspaces $4$
Sturm bound $60$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.k (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(60\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

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

Total New Old
Modular forms 128 128 0
Cusp forms 112 112 0
Eisenstein series 16 16 0

Trace form

\( 112 q - q^{2} - 4 q^{3} - 27 q^{4} - 5 q^{5} + q^{6} - 9 q^{7} + 7 q^{8} + 92 q^{9} + O(q^{10}) \) \( 112 q - q^{2} - 4 q^{3} - 27 q^{4} - 5 q^{5} + q^{6} - 9 q^{7} + 7 q^{8} + 92 q^{9} - 12 q^{10} - 6 q^{11} - 42 q^{12} + 2 q^{13} + 7 q^{14} - 14 q^{15} - 19 q^{16} - 2 q^{17} - 21 q^{18} + 5 q^{19} + 11 q^{20} - q^{21} - 14 q^{22} + 12 q^{23} - 18 q^{24} - 9 q^{25} - 23 q^{26} - 10 q^{27} + 13 q^{28} + 11 q^{29} + 30 q^{30} - 12 q^{31} - 82 q^{32} - 29 q^{33} - 8 q^{34} + 13 q^{35} - 10 q^{36} - 2 q^{37} - 41 q^{38} - 118 q^{39} + 79 q^{40} + 12 q^{41} - 27 q^{42} + 44 q^{43} + 31 q^{44} - 20 q^{45} + 31 q^{46} - 6 q^{47} + 96 q^{48} - 33 q^{49} + 14 q^{50} + 7 q^{51} + 31 q^{52} - 14 q^{53} - 17 q^{54} - 38 q^{55} - 19 q^{56} - 60 q^{57} + 56 q^{58} - 7 q^{59} - 29 q^{60} - 34 q^{61} + 32 q^{62} - 19 q^{63} - 45 q^{64} - 24 q^{65} - 7 q^{66} - 35 q^{67} + q^{68} - 26 q^{69} + 47 q^{70} - 4 q^{71} + 96 q^{72} - 20 q^{73} + q^{74} - 74 q^{75} - 130 q^{76} + 46 q^{77} + 11 q^{78} + 11 q^{79} + 111 q^{80} + 72 q^{81} - 50 q^{82} + 57 q^{83} + 16 q^{84} - 26 q^{85} + 11 q^{86} + 48 q^{87} - 14 q^{88} + 24 q^{89} - 191 q^{90} - 20 q^{91} + 82 q^{92} - 43 q^{93} + 70 q^{94} - 46 q^{95} - 170 q^{96} + 61 q^{97} + 112 q^{98} - 63 q^{99} + O(q^{100}) \)

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.k.a 275.k 275.k $4$ $2.196$ \(\Q(\zeta_{10})\) None \(-2\) \(-6\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}+\zeta_{10}^{3})q^{2}+(-2-\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
275.2.k.b 275.k 275.k $4$ $2.196$ \(\Q(\zeta_{10})\) None \(-2\) \(-6\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}+\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
275.2.k.c 275.k 275.k $4$ $2.196$ \(\Q(\zeta_{10})\) None \(1\) \(0\) \(5\) \(-10\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{3}q^{2}+(1+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{3}+\cdots\)
275.2.k.d 275.k 275.k $100$ $2.196$ None \(2\) \(8\) \(0\) \(5\) $\mathrm{SU}(2)[C_{5}]$