Properties

Label 2023.4.a
Level $2023$
Weight $4$
Character orbit 2023.a
Rep. character $\chi_{2023}(1,\cdot)$
Character field $\Q$
Dimension $407$
Newform subspaces $22$
Sturm bound $816$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(816\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2023))\).

Total New Old
Modular forms 630 407 223
Cusp forms 594 407 187
Eisenstein series 36 0 36

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.
\(+\)\(+\)\(+\)\(104\)
\(+\)\(-\)\(-\)\(100\)
\(-\)\(+\)\(-\)\(95\)
\(-\)\(-\)\(+\)\(108\)
Plus space\(+\)\(212\)
Minus space\(-\)\(195\)

Trace form

\( 407q - q^{2} - 6q^{3} + 1649q^{4} - 62q^{6} - 7q^{7} + 15q^{8} + 3759q^{9} + O(q^{10}) \) \( 407q - q^{2} - 6q^{3} + 1649q^{4} - 62q^{6} - 7q^{7} + 15q^{8} + 3759q^{9} - 128q^{10} - 60q^{11} - 34q^{12} - 28q^{13} + 7q^{14} + 96q^{15} + 6561q^{16} - 233q^{18} + 110q^{19} - 320q^{20} - 14q^{21} + 224q^{22} - 64q^{23} - 1158q^{24} + 9717q^{25} + 44q^{26} - 300q^{27} + 49q^{28} - 694q^{29} + 804q^{30} - 44q^{31} + 919q^{32} - 168q^{33} + 168q^{35} + 17437q^{36} + 234q^{37} + 982q^{38} + 640q^{39} + 724q^{40} - 542q^{41} + 14q^{42} - 572q^{43} + 56q^{44} + 112q^{45} - 168q^{46} + 1284q^{47} + 3162q^{48} + 19943q^{49} + 1409q^{50} + 232q^{52} - 422q^{53} + 1728q^{54} + 352q^{55} - 105q^{56} - 1180q^{57} - 1630q^{58} + 582q^{59} + 2884q^{60} - 568q^{61} + 4076q^{62} + 273q^{63} + 25633q^{64} - 384q^{65} + 3392q^{66} - 816q^{67} - 1000q^{69} - 616q^{70} - 232q^{71} + 455q^{72} + 838q^{73} - 42q^{74} - 922q^{75} - 2934q^{76} + 896q^{77} + 940q^{78} - 3160q^{79} - 720q^{80} + 33627q^{81} + 2842q^{82} - 618q^{83} + 98q^{84} + 2176q^{86} - 36q^{87} - 2860q^{88} - 4274q^{89} - 700q^{90} - 532q^{91} + 5512q^{92} + 2840q^{93} - 1888q^{94} - 1176q^{95} - 1070q^{96} + 194q^{97} - 49q^{98} - 6396q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2023))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 17
2023.4.a.a \(1\) \(119.361\) \(\Q\) None \(-1\) \(2\) \(-16\) \(7\) \(-\) \(+\) \(q-q^{2}+2q^{3}-7q^{4}-2^{4}q^{5}-2q^{6}+\cdots\)
2023.4.a.b \(1\) \(119.361\) \(\Q\) None \(-1\) \(6\) \(20\) \(7\) \(-\) \(+\) \(q-q^{2}+6q^{3}-7q^{4}+20q^{5}-6q^{6}+\cdots\)
2023.4.a.c \(1\) \(119.361\) \(\Q\) None \(3\) \(-1\) \(6\) \(-7\) \(+\) \(+\) \(q+3q^{2}-q^{3}+q^{4}+6q^{5}-3q^{6}-7q^{7}+\cdots\)
2023.4.a.d \(1\) \(119.361\) \(\Q\) None \(3\) \(1\) \(-6\) \(7\) \(-\) \(-\) \(q+3q^{2}+q^{3}+q^{4}-6q^{5}+3q^{6}+7q^{7}+\cdots\)
2023.4.a.e \(3\) \(119.361\) 3.3.2429.1 None \(-1\) \(-5\) \(19\) \(21\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
2023.4.a.f \(4\) \(119.361\) 4.4.68557.1 None \(-2\) \(7\) \(9\) \(-28\) \(+\) \(+\) \(q+(-1-\beta _{2})q^{2}+(2+\beta _{1}+\beta _{3})q^{3}+\cdots\)
2023.4.a.g \(7\) \(119.361\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(-5\) \(-35\) \(49\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots\)
2023.4.a.h \(9\) \(119.361\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(2\) \(-11\) \(3\) \(-63\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(4+\beta _{2})q^{4}+\cdots\)
2023.4.a.i \(11\) \(119.361\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-7\) \(-2\) \(2\) \(-77\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.4.a.j \(11\) \(119.361\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-7\) \(2\) \(-2\) \(77\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}+\beta _{3}q^{3}+(4-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2023.4.a.k \(12\) \(119.361\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(-3\) \(12\) \(84\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.4.a.l \(12\) \(119.361\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(3\) \(-12\) \(-84\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(5+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2023.4.a.m \(13\) \(119.361\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-14\) \(-20\) \(91\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots\)
2023.4.a.n \(13\) \(119.361\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(14\) \(20\) \(-91\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(5+\beta _{2})q^{4}+\cdots\)
2023.4.a.o \(26\) \(119.361\) None \(-8\) \(-12\) \(-40\) \(182\) \(-\) \(+\)
2023.4.a.p \(26\) \(119.361\) None \(-8\) \(12\) \(40\) \(-182\) \(+\) \(+\)
2023.4.a.q \(33\) \(119.361\) None \(-12\) \(0\) \(0\) \(-231\) \(+\) \(-\)
2023.4.a.r \(33\) \(119.361\) None \(-12\) \(0\) \(0\) \(231\) \(-\) \(+\)
2023.4.a.s \(39\) \(119.361\) None \(12\) \(0\) \(0\) \(273\) \(-\) \(-\)
2023.4.a.t \(39\) \(119.361\) None \(12\) \(0\) \(0\) \(-273\) \(+\) \(+\)
2023.4.a.u \(56\) \(119.361\) None \(8\) \(-24\) \(-80\) \(-392\) \(+\) \(-\)
2023.4.a.v \(56\) \(119.361\) None \(8\) \(24\) \(80\) \(392\) \(-\) \(-\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2023))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2023)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)