↑

Properties

Label 403.2.c
Level $403$
Weight $2$
Character orbit 403.c
Rep. character $\chi_{403}(311,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $2$
Sturm bound $74$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(403, [\chi])\).

Total New Old
Modular forms 38 34 4
Cusp forms 34 34 0
Eisenstein series 4 0 4

Trace form

\( 34 q - 32 q^{4} + 22 q^{9} + O(q^{10}) \) \( 34 q - 32 q^{4} + 22 q^{9} + 4 q^{10} - 8 q^{12} + 6 q^{13} - 16 q^{14} + 36 q^{16} - 12 q^{17} - 16 q^{22} - 16 q^{23} - 18 q^{25} + 18 q^{26} + 12 q^{27} + 40 q^{30} + 12 q^{35} - 40 q^{36} + 12 q^{38} - 4 q^{39} + 28 q^{40} + 28 q^{42} - 24 q^{43} + 16 q^{48} - 58 q^{49} - 8 q^{51} - 72 q^{52} - 20 q^{53} + 36 q^{55} + 8 q^{56} + 36 q^{61} + 8 q^{62} - 60 q^{64} - 42 q^{65} - 68 q^{66} + 56 q^{68} + 4 q^{69} + 16 q^{74} - 44 q^{75} - 28 q^{77} - 20 q^{78} + 32 q^{79} - 38 q^{81} + 12 q^{82} - 40 q^{87} + 80 q^{88} + 68 q^{90} + 10 q^{91} + 12 q^{92} + 88 q^{94} + 20 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
403.2.c.a 403.c 13.b $2$ $3.218$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{3}+2q^{4}+4iq^{5}-2iq^{7}+q^{9}+\cdots\)
403.2.c.b 403.c 13.b $32$ $3.218$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$