Properties

Label 1603.2.a
Level 1603
Weight 2
Character orbit a
Rep. character \(\chi_{1603}(1,\cdot)\)
Character field \(\Q\)
Dimension 115
Newforms 5
Sturm bound 306
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1603 = 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1603.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(306\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1603))\).

Total New Old
Modular forms 154 115 39
Cusp forms 151 115 36
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.

\(7\)\(229\)FrickeDim.
\(+\)\(+\)\(+\)\(26\)
\(+\)\(-\)\(-\)\(32\)
\(-\)\(+\)\(-\)\(31\)
\(-\)\(-\)\(+\)\(26\)
Plus space\(+\)\(52\)
Minus space\(-\)\(63\)

Trace form

\( 115q - q^{2} + 119q^{4} + 6q^{5} - 4q^{6} - q^{7} - 9q^{8} + 111q^{9} + O(q^{10}) \) \( 115q - q^{2} + 119q^{4} + 6q^{5} - 4q^{6} - q^{7} - 9q^{8} + 111q^{9} + 2q^{10} - 12q^{12} + 14q^{13} + q^{14} + 20q^{15} + 115q^{16} + 2q^{17} + 7q^{18} + 4q^{19} + 22q^{20} - 4q^{21} - 36q^{22} - 4q^{23} + 24q^{24} + 137q^{25} + 2q^{26} - 12q^{27} - 7q^{28} - 10q^{29} - 4q^{30} - 49q^{32} - 36q^{33} + 6q^{34} - 2q^{35} + 119q^{36} + 10q^{37} + 4q^{38} - 48q^{39} + 22q^{40} - 6q^{41} - 8q^{42} - 16q^{43} + 12q^{44} + 18q^{45} + 24q^{46} - 24q^{48} + 115q^{49} - 27q^{50} - 24q^{51} + 26q^{52} + 30q^{53} - 32q^{54} - 4q^{55} - 3q^{56} - 16q^{57} + 10q^{58} - 32q^{59} - 4q^{60} + 26q^{61} - 40q^{62} + 3q^{63} + 83q^{64} - 8q^{65} - 64q^{66} - 4q^{67} - 46q^{68} + 28q^{69} - 14q^{70} + 8q^{71} - 57q^{72} + 6q^{73} - 30q^{74} - 12q^{75} - 4q^{76} - 12q^{77} - 92q^{78} - 4q^{79} + 14q^{80} + 91q^{81} - 42q^{82} - 56q^{83} + 28q^{85} - 100q^{86} + 20q^{87} - 148q^{88} + 30q^{89} - 54q^{90} + 2q^{91} + 8q^{92} - 8q^{93} - 20q^{94} - 36q^{95} + 72q^{96} - 18q^{97} - q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1603))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 229
1603.2.a.a \(3\) \(12.800\) 3.3.169.1 None \(-1\) \(3\) \(0\) \(-3\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1603.2.a.b \(23\) \(12.800\) None \(-7\) \(-5\) \(-15\) \(-23\) \(+\) \(+\)
1603.2.a.c \(26\) \(12.800\) None \(-6\) \(-14\) \(-25\) \(26\) \(-\) \(-\)
1603.2.a.d \(31\) \(12.800\) None \(6\) \(12\) \(27\) \(31\) \(-\) \(+\)
1603.2.a.e \(32\) \(12.800\) None \(7\) \(4\) \(19\) \(-32\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1603))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1603)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(229))\)\(^{\oplus 2}\)