Properties

Label 46.2.c
Level $46$
Weight $2$
Character orbit 46.c
Rep. character $\chi_{46}(3,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $20$
Newform subspaces $2$
Sturm bound $12$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 46 = 2 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 46.c (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(46, [\chi])\).

Total New Old
Modular forms 80 20 60
Cusp forms 40 20 20
Eisenstein series 40 0 40

Trace form

\( 20 q - 4 q^{3} - 2 q^{4} - 10 q^{5} - 4 q^{6} - 4 q^{7} - 10 q^{9} + O(q^{10}) \) \( 20 q - 4 q^{3} - 2 q^{4} - 10 q^{5} - 4 q^{6} - 4 q^{7} - 10 q^{9} - 2 q^{10} - 14 q^{11} - 4 q^{12} - 12 q^{13} - 12 q^{14} - 2 q^{15} - 2 q^{16} + 6 q^{17} + 28 q^{18} + 4 q^{19} + 12 q^{20} + 34 q^{21} + 12 q^{22} + 20 q^{23} - 4 q^{24} + 2 q^{25} + 6 q^{26} + 26 q^{27} + 18 q^{28} - 10 q^{29} + 20 q^{30} - 10 q^{31} - 26 q^{33} - 20 q^{34} - 10 q^{35} - 10 q^{36} + 10 q^{37} - 22 q^{38} - 12 q^{39} - 2 q^{40} - 26 q^{41} - 32 q^{42} - 10 q^{43} - 14 q^{44} - 22 q^{46} - 4 q^{47} - 4 q^{48} - 20 q^{50} - 28 q^{51} - 12 q^{52} - 28 q^{53} - 18 q^{54} + 8 q^{55} + 10 q^{56} + 30 q^{57} + 16 q^{58} + 38 q^{59} - 2 q^{60} + 34 q^{61} + 34 q^{62} - 6 q^{63} - 2 q^{64} + 78 q^{65} + 40 q^{66} - 14 q^{67} + 28 q^{68} + 18 q^{69} + 24 q^{70} + 38 q^{71} + 28 q^{72} - 36 q^{73} + 46 q^{74} + 52 q^{75} - 18 q^{76} + 22 q^{77} + 10 q^{78} + 42 q^{79} + 12 q^{80} + 2 q^{81} + 8 q^{82} - 10 q^{83} - 10 q^{84} - 34 q^{85} - 12 q^{86} - 54 q^{87} - 10 q^{88} - 62 q^{89} - 90 q^{90} - 76 q^{91} - 24 q^{92} - 128 q^{93} - 48 q^{94} - 46 q^{95} - 4 q^{96} - 16 q^{97} - 4 q^{98} + 26 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(46, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
46.2.c.a \(10\) \(0.367\) \(\Q(\zeta_{22})\) None \(-1\) \(-4\) \(-6\) \(3\) \(q-\zeta_{22}q^{2}+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{7}+\cdots)q^{3}+\cdots\)
46.2.c.b \(10\) \(0.367\) \(\Q(\zeta_{22})\) None \(1\) \(0\) \(-4\) \(-7\) \(q+\zeta_{22}q^{2}+(-\zeta_{22}+\zeta_{22}^{4}+\zeta_{22}^{7}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(46, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(46, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)