Properties

Label 14.5.b
Level 14
Weight 5
Character orbit b
Rep. character \(\chi_{14}(13,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 1
Sturm bound 10
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 14.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(14, [\chi])\).

Total New Old
Modular forms 10 4 6
Cusp forms 6 4 2
Eisenstein series 4 0 4

Trace form

\(4q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut -\mathstrut 76q^{7} \) \(\mathstrut -\mathstrut 252q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut -\mathstrut 76q^{7} \) \(\mathstrut -\mathstrut 252q^{9} \) \(\mathstrut +\mathstrut 360q^{11} \) \(\mathstrut -\mathstrut 288q^{14} \) \(\mathstrut +\mathstrut 384q^{15} \) \(\mathstrut +\mathstrut 256q^{16} \) \(\mathstrut +\mathstrut 192q^{18} \) \(\mathstrut +\mathstrut 768q^{21} \) \(\mathstrut -\mathstrut 1152q^{22} \) \(\mathstrut -\mathstrut 792q^{23} \) \(\mathstrut -\mathstrut 2300q^{25} \) \(\mathstrut -\mathstrut 608q^{28} \) \(\mathstrut +\mathstrut 1224q^{29} \) \(\mathstrut +\mathstrut 4416q^{30} \) \(\mathstrut +\mathstrut 4032q^{35} \) \(\mathstrut -\mathstrut 2016q^{36} \) \(\mathstrut -\mathstrut 3896q^{37} \) \(\mathstrut -\mathstrut 768q^{39} \) \(\mathstrut -\mathstrut 4800q^{42} \) \(\mathstrut +\mathstrut 3688q^{43} \) \(\mathstrut +\mathstrut 2880q^{44} \) \(\mathstrut +\mathstrut 3072q^{46} \) \(\mathstrut -\mathstrut 1532q^{49} \) \(\mathstrut -\mathstrut 7488q^{50} \) \(\mathstrut -\mathstrut 11136q^{51} \) \(\mathstrut +\mathstrut 5832q^{53} \) \(\mathstrut -\mathstrut 2304q^{56} \) \(\mathstrut +\mathstrut 12864q^{57} \) \(\mathstrut +\mathstrut 7296q^{58} \) \(\mathstrut +\mathstrut 3072q^{60} \) \(\mathstrut +\mathstrut 3060q^{63} \) \(\mathstrut +\mathstrut 2048q^{64} \) \(\mathstrut -\mathstrut 4032q^{65} \) \(\mathstrut -\mathstrut 1048q^{67} \) \(\mathstrut -\mathstrut 1344q^{70} \) \(\mathstrut -\mathstrut 21528q^{71} \) \(\mathstrut +\mathstrut 1536q^{72} \) \(\mathstrut -\mathstrut 3456q^{74} \) \(\mathstrut +\mathstrut 3528q^{77} \) \(\mathstrut +\mathstrut 4800q^{78} \) \(\mathstrut +\mathstrut 12776q^{79} \) \(\mathstrut -\mathstrut 29628q^{81} \) \(\mathstrut +\mathstrut 6144q^{84} \) \(\mathstrut +\mathstrut 16512q^{85} \) \(\mathstrut -\mathstrut 11520q^{86} \) \(\mathstrut -\mathstrut 9216q^{88} \) \(\mathstrut +\mathstrut 5568q^{91} \) \(\mathstrut -\mathstrut 6336q^{92} \) \(\mathstrut +\mathstrut 38016q^{93} \) \(\mathstrut +\mathstrut 36864q^{95} \) \(\mathstrut +\mathstrut 21888q^{98} \) \(\mathstrut -\mathstrut 29592q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(14, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
14.5.b.a \(4\) \(1.447\) 4.0.1308672.3 None \(0\) \(0\) \(0\) \(-76\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+8q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)