Properties

Label 2023.2.a
Level $2023$
Weight $2$
Character orbit 2023.a
Rep. character $\chi_{2023}(1,\cdot)$
Character field $\Q$
Dimension $135$
Newform subspaces $18$
Sturm bound $408$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2023.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(408\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2023))\).

Total New Old
Modular forms 222 135 87
Cusp forms 187 135 52
Eisenstein series 35 0 35

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

\(7\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(31\)
\(+\)\(-\)\(-\)\(36\)
\(-\)\(+\)\(-\)\(40\)
\(-\)\(-\)\(+\)\(28\)
Plus space\(+\)\(59\)
Minus space\(-\)\(76\)

Trace form

\( 135 q - q^{2} + 131 q^{4} - 2 q^{5} + q^{7} + 3 q^{8} + 127 q^{9} + O(q^{10}) \) \( 135 q - q^{2} + 131 q^{4} - 2 q^{5} + q^{7} + 3 q^{8} + 127 q^{9} - 2 q^{10} + 16 q^{12} - 14 q^{13} + 3 q^{14} + 4 q^{15} + 135 q^{16} + 19 q^{18} - 20 q^{19} + 22 q^{20} - 4 q^{21} + 16 q^{22} + 16 q^{23} + 24 q^{24} + 121 q^{25} + 30 q^{26} + 24 q^{27} + 7 q^{28} + 6 q^{29} + 36 q^{30} - 12 q^{31} - 5 q^{32} - 8 q^{33} - 2 q^{35} + 115 q^{36} - 14 q^{37} + 8 q^{38} + 4 q^{39} - 22 q^{40} - 30 q^{41} - 12 q^{42} - 8 q^{44} + 2 q^{45} - 32 q^{46} + 8 q^{47} + 12 q^{48} + 135 q^{49} - 35 q^{50} - 46 q^{52} + 22 q^{53} - 28 q^{54} + 15 q^{56} - 36 q^{57} + 10 q^{58} - 4 q^{59} - 36 q^{60} - 34 q^{61} - 32 q^{62} + 5 q^{63} + 143 q^{64} + 4 q^{65} - 48 q^{66} - 20 q^{67} + 16 q^{69} + 6 q^{70} + 16 q^{71} - 25 q^{72} - 30 q^{73} + 22 q^{74} + 44 q^{75} - 48 q^{76} - 4 q^{77} - 12 q^{78} - 4 q^{79} + 14 q^{80} + 103 q^{81} + 14 q^{82} + 32 q^{83} - 28 q^{84} - 68 q^{86} + 4 q^{87} + 68 q^{88} - 18 q^{89} - 70 q^{90} - 6 q^{91} - 32 q^{92} + 40 q^{93} + 12 q^{94} + 36 q^{95} - 38 q^{97} - q^{98} + 60 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2023))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 17
2023.2.a.a \(1\) \(16.154\) \(\Q\) None \(-1\) \(-3\) \(-4\) \(1\) \(-\) \(+\) \(q-q^{2}-3q^{3}-q^{4}-4q^{5}+3q^{6}+q^{7}+\cdots\)
2023.2.a.b \(1\) \(16.154\) \(\Q\) None \(-1\) \(3\) \(4\) \(-1\) \(+\) \(-\) \(q-q^{2}+3q^{3}-q^{4}+4q^{5}-3q^{6}-q^{7}+\cdots\)
2023.2.a.c \(3\) \(16.154\) 3.3.148.1 None \(-1\) \(-1\) \(-2\) \(-3\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.2.a.d \(3\) \(16.154\) 3.3.148.1 None \(-1\) \(1\) \(2\) \(3\) \(-\) \(-\) \(q-\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.2.a.e \(4\) \(16.154\) 4.4.9301.1 None \(-1\) \(-2\) \(-2\) \(-4\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.f \(4\) \(16.154\) 4.4.2225.1 None \(3\) \(-2\) \(-4\) \(-4\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.g \(4\) \(16.154\) 4.4.2225.1 None \(3\) \(2\) \(4\) \(4\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.h \(5\) \(16.154\) 5.5.240133.1 None \(2\) \(0\) \(-4\) \(-5\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.i \(5\) \(16.154\) 5.5.240133.1 None \(2\) \(0\) \(4\) \(5\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{4})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.2.a.j \(5\) \(16.154\) 5.5.453749.1 None \(2\) \(2\) \(0\) \(5\) \(-\) \(+\) \(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(2-\beta _{3})q^{4}+\cdots\)
2023.2.a.k \(9\) \(16.154\) 9.9.\(\cdots\).1 None \(-6\) \(0\) \(0\) \(9\) \(-\) \(-\) \(q+(-1-\beta _{5})q^{2}-\beta _{4}q^{3}+(1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
2023.2.a.l \(9\) \(16.154\) 9.9.\(\cdots\).1 None \(-6\) \(0\) \(0\) \(-9\) \(+\) \(+\) \(q+(-1-\beta _{5})q^{2}+\beta _{4}q^{3}+(1-\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
2023.2.a.m \(10\) \(16.154\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-4\) \(-8\) \(-10\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(2+\beta _{7}-\beta _{8})q^{4}+\cdots\)
2023.2.a.n \(10\) \(16.154\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(4\) \(8\) \(10\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{7}-\beta _{8})q^{4}+\cdots\)
2023.2.a.o \(15\) \(16.154\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(6\) \(0\) \(0\) \(15\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{13})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.2.a.p \(15\) \(16.154\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(6\) \(0\) \(0\) \(-15\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{13})q^{3}+(1+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
2023.2.a.q \(16\) \(16.154\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(-8\) \(-16\) \(16\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2023.2.a.r \(16\) \(16.154\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(8\) \(16\) \(-16\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2023))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)