↑

Properties

Label 637.2.bb
Level $637$
Weight $2$
Character orbit 637.bb
Rep. character $\chi_{637}(227,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $172$
Newform subspaces $3$
Sturm bound $130$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(130\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(637, [\chi])\).

Total New Old
Modular forms 292 204 88
Cusp forms 228 172 56
Eisenstein series 64 32 32

Trace form

\( 172 q + 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 20 q^{8} + 70 q^{9} + O(q^{10}) \) \( 172 q + 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 20 q^{8} + 70 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} - 46 q^{15} - 132 q^{16} + 12 q^{17} + 6 q^{18} - 14 q^{19} - 36 q^{20} - 4 q^{22} + 18 q^{24} - 24 q^{26} - 4 q^{29} + 54 q^{30} + 4 q^{31} - 58 q^{32} + 12 q^{33} + 12 q^{34} - 138 q^{36} - 18 q^{37} + 108 q^{39} - 48 q^{40} + 18 q^{41} + 118 q^{44} + 6 q^{45} + 16 q^{46} + 6 q^{47} + 12 q^{48} - 90 q^{50} - 120 q^{51} + 26 q^{52} - 8 q^{53} + 30 q^{54} - 6 q^{55} + 16 q^{57} + 142 q^{58} - 42 q^{59} + 66 q^{60} - 30 q^{61} - 36 q^{62} - 36 q^{65} - 66 q^{66} - 18 q^{67} + 42 q^{69} + 10 q^{71} - 38 q^{72} - 40 q^{73} - 148 q^{74} + 40 q^{75} + 52 q^{76} + 22 q^{78} - 20 q^{79} - 30 q^{80} + 14 q^{81} + 54 q^{82} - 66 q^{83} + 102 q^{85} + 50 q^{86} - 66 q^{88} - 72 q^{90} + 188 q^{92} - 128 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(637, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
637.2.bb.a 637.bb 91.aa $28$ $5.086$ None \(-2\) \(6\) \(6\) \(0\) $\mathrm{SU}(2)[C_{12}]$
637.2.bb.b 637.bb 91.aa $32$ $5.086$ None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
637.2.bb.c 637.bb 91.aa $112$ $5.086$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(637, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(637, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)