↑

Properties

Label 385.2.i
Level $385$
Weight $2$
Character orbit 385.i
Rep. character $\chi_{385}(221,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $56$
Newform subspaces $4$
Sturm bound $96$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 385 = 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 385.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(385, [\chi])\).

Total New Old
Modular forms 104 56 48
Cusp forms 88 56 32
Eisenstein series 16 0 16

Trace form

\( 56 q + 4 q^{3} - 32 q^{4} + 4 q^{5} + 8 q^{6} - 4 q^{7} - 36 q^{9} + O(q^{10}) \) \( 56 q + 4 q^{3} - 32 q^{4} + 4 q^{5} + 8 q^{6} - 4 q^{7} - 36 q^{9} - 12 q^{12} + 32 q^{13} + 4 q^{14} - 44 q^{16} - 20 q^{18} + 4 q^{19} - 16 q^{20} - 20 q^{21} + 28 q^{24} - 28 q^{25} - 12 q^{26} - 32 q^{27} + 20 q^{28} + 32 q^{29} - 4 q^{30} - 24 q^{31} - 40 q^{32} + 8 q^{33} + 24 q^{34} + 4 q^{35} + 160 q^{36} - 8 q^{37} + 44 q^{38} - 12 q^{39} - 8 q^{41} + 48 q^{42} - 24 q^{43} - 4 q^{44} - 16 q^{46} + 12 q^{47} - 32 q^{48} + 24 q^{49} - 8 q^{51} - 40 q^{52} + 12 q^{53} - 48 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 20 q^{58} - 4 q^{59} - 4 q^{61} + 56 q^{62} - 28 q^{63} + 128 q^{64} - 20 q^{66} + 8 q^{67} + 16 q^{68} - 24 q^{69} + 4 q^{70} - 24 q^{71} + 16 q^{72} + 4 q^{73} + 40 q^{74} + 4 q^{75} + 8 q^{76} + 4 q^{77} - 136 q^{78} + 16 q^{79} + 20 q^{80} - 52 q^{81} + 12 q^{82} + 112 q^{83} + 12 q^{84} + 8 q^{85} - 64 q^{86} + 48 q^{87} - 40 q^{89} + 72 q^{90} + 12 q^{91} + 36 q^{93} - 12 q^{94} + 56 q^{96} - 120 q^{97} + 52 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(385, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
385.2.i.a 385.i 7.c $8$ $3.074$ 8.0.310217769.2 None \(3\) \(3\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2}-\beta _{5}-\beta _{7})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)
385.2.i.b 385.i 7.c $12$ $3.074$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(-1\) \(6\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{9}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
385.2.i.c 385.i 7.c $16$ $3.074$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(-1\) \(-8\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-\beta _{8}+\beta _{11}+\cdots)q^{4}+\cdots\)
385.2.i.d 385.i 7.c $20$ $3.074$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-3\) \(3\) \(10\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{10}+\beta _{17})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(385, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(385, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)