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Properties

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

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Defining parameters

Level: \( N \) \(=\) \( 1603 = 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1603.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1603))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 229
1603.2.a.a 1603.a 1.a $3$ $12.800$ 3.3.169.1 None \(-1\) \(3\) \(0\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1603.2.a.b 1603.a 1.a $23$ $12.800$ None \(-7\) \(-5\) \(-15\) \(-23\) $+$ $+$ $\mathrm{SU}(2)$
1603.2.a.c 1603.a 1.a $26$ $12.800$ None \(-6\) \(-14\) \(-25\) \(26\) $-$ $-$ $\mathrm{SU}(2)$
1603.2.a.d 1603.a 1.a $31$ $12.800$ None \(6\) \(12\) \(27\) \(31\) $-$ $+$ $\mathrm{SU}(2)$
1603.2.a.e 1603.a 1.a $32$ $12.800$ None \(7\) \(4\) \(19\) \(-32\) $+$ $-$ $\mathrm{SU}(2)$

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

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