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Properties

Label 345.2.m
Level $345$
Weight $2$
Character orbit 345.m
Rep. character $\chi_{345}(16,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $160$
Newform subspaces $4$
Sturm bound $96$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 345 = 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 345.m (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(345, [\chi])\).

Total New Old
Modular forms 520 160 360
Cusp forms 440 160 280
Eisenstein series 80 0 80

Trace form

\( 160 q + 8 q^{2} - 4 q^{4} + 4 q^{6} + 8 q^{7} + 24 q^{8} - 16 q^{9} + O(q^{10}) \) \( 160 q + 8 q^{2} - 4 q^{4} + 4 q^{6} + 8 q^{7} + 24 q^{8} - 16 q^{9} + 8 q^{10} + 32 q^{11} + 8 q^{13} + 16 q^{14} + 4 q^{15} - 68 q^{16} - 28 q^{17} + 8 q^{18} - 20 q^{19} - 64 q^{22} + 24 q^{23} + 12 q^{24} - 16 q^{25} - 24 q^{26} + 64 q^{28} + 4 q^{30} + 8 q^{32} + 8 q^{33} + 10 q^{34} - 32 q^{35} - 48 q^{36} + 64 q^{37} - 148 q^{38} - 36 q^{39} + 2 q^{40} - 36 q^{41} + 24 q^{42} - 40 q^{43} + 60 q^{44} - 104 q^{46} + 56 q^{47} - 144 q^{48} + 36 q^{49} - 36 q^{50} - 56 q^{51} + 64 q^{52} - 32 q^{53} - 18 q^{54} - 28 q^{55} - 132 q^{56} + 8 q^{57} - 20 q^{58} + 16 q^{59} - 10 q^{60} + 4 q^{61} + 64 q^{62} + 8 q^{63} + 28 q^{64} + 32 q^{65} + 56 q^{66} + 20 q^{67} + 152 q^{68} + 24 q^{69} + 100 q^{71} + 24 q^{72} + 28 q^{73} + 60 q^{74} + 56 q^{76} - 120 q^{77} + 16 q^{78} - 132 q^{79} + 32 q^{80} - 16 q^{81} - 184 q^{82} - 112 q^{83} + 48 q^{84} + 20 q^{85} + 136 q^{86} + 8 q^{87} - 144 q^{88} - 160 q^{89} + 8 q^{90} + 80 q^{91} - 228 q^{92} + 16 q^{93} - 220 q^{94} + 16 q^{95} - 16 q^{96} - 168 q^{97} - 144 q^{98} + 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(345, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
345.2.m.a 345.m 23.c $30$ $2.755$ None \(0\) \(3\) \(3\) \(1\) $\mathrm{SU}(2)[C_{11}]$
345.2.m.b 345.m 23.c $30$ $2.755$ None \(6\) \(-3\) \(-3\) \(7\) $\mathrm{SU}(2)[C_{11}]$
345.2.m.c 345.m 23.c $50$ $2.755$ None \(0\) \(-5\) \(5\) \(-3\) $\mathrm{SU}(2)[C_{11}]$
345.2.m.d 345.m 23.c $50$ $2.755$ None \(2\) \(5\) \(-5\) \(3\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(345, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(345, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)