↑

Properties

Label 4.14.a
Level $4$
Weight $14$
Character orbit 4.a
Rep. character $\chi_{4}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 4.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(4))\).

Total New Old
Modular forms 8 1 7
Cusp forms 5 1 4
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim
\(-\)\(1\)

Trace form

\( q + 468 q^{3} + 56214 q^{5} + 333032 q^{7} - 1375299 q^{9} + O(q^{10}) \) \( q + 468 q^{3} + 56214 q^{5} + 333032 q^{7} - 1375299 q^{9} - 6397380 q^{11} + 15199742 q^{13} + 26308152 q^{15} + 43114194 q^{17} - 365115484 q^{19} + 155858976 q^{21} - 57226824 q^{23} + 1939310671 q^{25} - 1389783096 q^{27} - 46418994 q^{29} - 5682185824 q^{31} - 2993973840 q^{33} + 18721060848 q^{35} - 1887185098 q^{37} + 7113479256 q^{39} - 7336802934 q^{41} - 26886674980 q^{43} - 77311057986 q^{45} + 101839834224 q^{47} + 14021302617 q^{49} + 20177442792 q^{51} + 278731884294 q^{53} - 359622319320 q^{55} - 170874046512 q^{57} + 59573945772 q^{59} - 27484470418 q^{61} - 458018576568 q^{63} + 854438296788 q^{65} + 784410054932 q^{67} - 26782153632 q^{69} - 360365227992 q^{71} - 1592635413718 q^{73} + 907597394028 q^{75} - 2130532256160 q^{77} - 23161184752 q^{79} + 1542252338649 q^{81} + 2050158110436 q^{83} + 2423621301516 q^{85} - 21724089192 q^{87} - 3485391237126 q^{89} + 5062000477744 q^{91} - 2659262965632 q^{93} - 20524601817576 q^{95} + 6706667416802 q^{97} + 8798310316620 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(4))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
4.14.a.a 4.a 1.a $1$ $4.289$ \(\Q\) None \(0\) \(468\) \(56214\) \(333032\) $-$ $\mathrm{SU}(2)$ \(q+468q^{3}+56214q^{5}+333032q^{7}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(4))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(4)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)