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Properties

Label 775.2.bl
Level $775$
Weight $2$
Character orbit 775.bl
Rep. character $\chi_{775}(51,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $384$
Newform subspaces $6$
Sturm bound $160$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.bl (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 6 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(775, [\chi])\).

Total New Old
Modular forms 688 432 256
Cusp forms 592 384 208
Eisenstein series 96 48 48

Trace form

\( 384 q + 6 q^{2} + 10 q^{3} - 82 q^{4} - 21 q^{6} - 4 q^{7} + q^{8} + 54 q^{9} + O(q^{10}) \) \( 384 q + 6 q^{2} + 10 q^{3} - 82 q^{4} - 21 q^{6} - 4 q^{7} + q^{8} + 54 q^{9} - 17 q^{11} + 9 q^{12} + 11 q^{13} + 38 q^{14} - 110 q^{16} + 12 q^{17} - 7 q^{18} - 12 q^{19} + 23 q^{21} - 9 q^{22} + 15 q^{23} + 52 q^{24} - 45 q^{26} + q^{27} - 30 q^{28} + 6 q^{29} - 51 q^{31} + 98 q^{32} - 9 q^{33} + 50 q^{34} - 155 q^{36} + 34 q^{37} - 6 q^{38} - 63 q^{39} - 48 q^{41} + 63 q^{42} + 29 q^{43} + 53 q^{44} - 58 q^{46} - 14 q^{47} - 98 q^{48} - 28 q^{49} + 50 q^{51} - 93 q^{52} - 8 q^{53} - 66 q^{54} + 56 q^{56} + 15 q^{57} + 41 q^{58} - 40 q^{59} + 32 q^{61} + 13 q^{62} - 54 q^{63} - 161 q^{64} + 66 q^{66} - 41 q^{67} + 32 q^{68} + 30 q^{69} - 6 q^{71} - 227 q^{72} - 4 q^{73} - 35 q^{74} + 98 q^{76} + 10 q^{77} + 39 q^{78} + 44 q^{79} - 17 q^{81} + 50 q^{82} + 34 q^{83} - 106 q^{84} - 176 q^{86} + 67 q^{87} + 71 q^{88} - 57 q^{89} - 76 q^{91} - 36 q^{92} + 43 q^{93} + 264 q^{94} + 24 q^{96} - 31 q^{97} + 88 q^{98} - 112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
775.2.bl.a 775.bl 31.g $16$ $6.188$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(6\) \(12\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{15}]$ \(q+(-\beta _{1}-\beta _{4}+\beta _{5}-\beta _{9}-\beta _{10}-\beta _{11}+\cdots)q^{2}+\cdots\)
775.2.bl.b 775.bl 31.g $40$ $6.188$ None \(-2\) \(-3\) \(0\) \(2\) $\mathrm{SU}(2)[C_{15}]$
775.2.bl.c 775.bl 31.g $40$ $6.188$ None \(2\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{15}]$
775.2.bl.d 775.bl 31.g $88$ $6.188$ None \(0\) \(-3\) \(0\) \(2\) $\mathrm{SU}(2)[C_{15}]$
775.2.bl.e 775.bl 31.g $88$ $6.188$ None \(0\) \(3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{15}]$
775.2.bl.f 775.bl 31.g $112$ $6.188$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{15}]$

Decomposition of \(S_{2}^{\mathrm{old}}(775, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(775, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)