Properties

Label 414.2.m
Level $414$
Weight $2$
Character orbit 414.m
Rep. character $\chi_{414}(13,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $480$
Newform subspaces $2$
Sturm bound $144$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 414.m (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{33})\)
Newform subspaces: \( 2 \)
Sturm bound: \(144\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(414, [\chi])\).

Total New Old
Modular forms 1520 480 1040
Cusp forms 1360 480 880
Eisenstein series 160 0 160

Trace form

\( 480 q + 4 q^{3} + 24 q^{4} - 8 q^{6} + 8 q^{9} + O(q^{10}) \) \( 480 q + 4 q^{3} + 24 q^{4} - 8 q^{6} + 8 q^{9} + 4 q^{11} + 4 q^{12} + 4 q^{14} + 24 q^{15} + 24 q^{16} - 16 q^{17} - 28 q^{18} - 62 q^{21} - 6 q^{23} + 4 q^{24} + 12 q^{25} + 16 q^{26} - 86 q^{27} - 16 q^{29} - 32 q^{30} - 12 q^{31} + 32 q^{33} - 16 q^{36} + 24 q^{37} + 12 q^{38} + 48 q^{39} + 4 q^{41} + 20 q^{42} - 8 q^{44} + 16 q^{45} + 12 q^{46} + 8 q^{47} - 8 q^{48} + 78 q^{49} - 8 q^{50} - 40 q^{51} + 32 q^{53} - 30 q^{54} + 24 q^{55} + 26 q^{56} - 82 q^{57} - 168 q^{59} - 6 q^{60} - 12 q^{61} - 108 q^{62} - 134 q^{63} - 48 q^{64} + 134 q^{65} - 88 q^{66} - 12 q^{67} - 80 q^{68} - 110 q^{69} - 12 q^{70} - 244 q^{71} - 52 q^{72} + 80 q^{74} - 144 q^{75} - 216 q^{77} - 50 q^{78} - 44 q^{80} + 32 q^{81} + 102 q^{83} - 6 q^{84} - 16 q^{86} - 154 q^{87} - 96 q^{89} - 28 q^{90} - 6 q^{92} - 36 q^{93} - 12 q^{94} + 12 q^{95} + 4 q^{96} + 54 q^{97} + 16 q^{98} + 84 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(414, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
414.2.m.a 414.m 207.m $240$ $3.306$ None \(-12\) \(0\) \(0\) \(-13\) $\mathrm{SU}(2)[C_{33}]$
414.2.m.b 414.m 207.m $240$ $3.306$ None \(12\) \(4\) \(0\) \(13\) $\mathrm{SU}(2)[C_{33}]$

Decomposition of \(S_{2}^{\mathrm{old}}(414, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(414, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)