Properties

Label 403.2.a
Level 403
Weight 2
Character orbit a
Rep. character \(\chi_{403}(1,\cdot)\)
Character field \(\Q\)
Dimension 31
Newforms 5
Sturm bound 74
Trace bound 2

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(74\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(403))\).

Total New Old
Modular forms 38 31 7
Cusp forms 35 31 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.

\(13\)\(31\)FrickeDim.
\(+\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(14\)
Minus space\(-\)\(17\)

Trace form

\( 31q - 3q^{2} + 33q^{4} - 2q^{5} - 9q^{8} + 23q^{9} + O(q^{10}) \) \( 31q - 3q^{2} + 33q^{4} - 2q^{5} - 9q^{8} + 23q^{9} + 4q^{10} - 4q^{11} - 12q^{12} + q^{13} - 14q^{14} + 12q^{15} + 25q^{16} - 14q^{17} - 39q^{18} - 4q^{19} - 20q^{20} - 12q^{21} - 8q^{22} - 4q^{23} - 24q^{24} + 57q^{25} + 3q^{26} + 12q^{27} - 26q^{28} - 14q^{29} - 4q^{30} - 5q^{31} - 11q^{32} - 6q^{34} + 4q^{35} + 29q^{36} + 2q^{37} + 2q^{38} - 4q^{39} + 22q^{40} - 14q^{41} + 8q^{42} - 16q^{43} + 8q^{44} - 22q^{45} - 4q^{47} - 40q^{48} + 11q^{49} + 13q^{50} - 8q^{51} - q^{52} + 26q^{53} + 28q^{54} - 4q^{55} - 12q^{56} - 40q^{57} + 18q^{58} - 24q^{59} + 92q^{60} + 6q^{61} + 3q^{62} - 44q^{63} + 3q^{64} + 6q^{65} + 4q^{66} - 36q^{67} - 2q^{68} + 12q^{69} + 2q^{70} - 12q^{71} - 21q^{72} + 6q^{73} + 38q^{74} - 56q^{75} - 10q^{76} - 52q^{77} - 12q^{78} - 12q^{79} + 4q^{80} - 9q^{81} + 12q^{82} - 8q^{83} - 4q^{84} + 32q^{85} - 20q^{86} - 4q^{88} - 2q^{89} + 36q^{90} - 76q^{92} + 24q^{94} + 12q^{95} - 4q^{96} - 22q^{97} + 99q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(403))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 13 31
403.2.a.a \(2\) \(3.218\) \(\Q(\sqrt{5}) \) None \(3\) \(-4\) \(0\) \(2\) \(-\) \(+\) \(q+(1+\beta )q^{2}-2q^{3}+3\beta q^{4}+(-1+2\beta )q^{5}+\cdots\)
403.2.a.b \(6\) \(3.218\) 6.6.5748973.1 None \(-2\) \(-5\) \(-9\) \(0\) \(-\) \(-\) \(q+\beta _{4}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
403.2.a.c \(7\) \(3.218\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(5\) \(11\) \(4\) \(+\) \(-\) \(q+\beta _{3}q^{2}+(1-\beta _{1})q^{3}+(\beta _{1}+\beta _{4}+\beta _{6})q^{4}+\cdots\)
403.2.a.d \(8\) \(3.218\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-5\) \(-3\) \(-15\) \(-4\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}-\beta _{6}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
403.2.a.e \(8\) \(3.218\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(7\) \(11\) \(-2\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(403))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(403)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)