Properties

Label 169.4.e
Level $169$
Weight $4$
Character orbit 169.e
Rep. character $\chi_{169}(23,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $8$
Sturm bound $60$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(60\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(169, [\chi])\).

Total New Old
Modular forms 104 88 16
Cusp forms 76 68 8
Eisenstein series 28 20 8

Trace form

\( 68q + 3q^{2} - 5q^{3} + 121q^{4} + 48q^{6} - 15q^{7} - 217q^{9} + O(q^{10}) \) \( 68q + 3q^{2} - 5q^{3} + 121q^{4} + 48q^{6} - 15q^{7} - 217q^{9} - 87q^{10} + 15q^{11} - 52q^{12} + 140q^{14} - 174q^{15} - 403q^{16} + 142q^{17} + 351q^{19} + 111q^{20} - 238q^{22} - 65q^{23} - 246q^{24} - 646q^{25} - 170q^{27} - 276q^{28} - 272q^{29} + 354q^{30} + 603q^{32} + 321q^{33} - 370q^{35} - 337q^{36} + 318q^{37} + 116q^{38} + 510q^{40} + 210q^{41} + 536q^{42} - 121q^{43} - 597q^{45} - 576q^{46} + 972q^{48} - 15q^{49} - 768q^{50} - 342q^{51} - 1378q^{53} + 510q^{54} - 288q^{55} - 710q^{56} - 9q^{58} + 525q^{59} + 326q^{61} + 916q^{62} + 1410q^{63} + 1594q^{64} + 360q^{66} + 1077q^{67} + 1527q^{68} - 931q^{69} - 2841q^{71} - 1425q^{72} + 565q^{74} + 1399q^{75} - 378q^{76} + 1494q^{77} + 232q^{79} - 1923q^{80} + 1138q^{81} - 1371q^{82} - 852q^{84} - 297q^{85} + 1033q^{87} - 816q^{88} + 1161q^{89} + 5414q^{90} + 2812q^{92} + 1422q^{93} + 2474q^{94} + 670q^{95} - 2487q^{97} + 1437q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(169, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
169.4.e.a \(2\) \(9.971\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-2\) \(0\) \(24\) \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{4}+\cdots\)
169.4.e.b \(2\) \(9.971\) \(\Q(\sqrt{-3}) \) None \(6\) \(7\) \(0\) \(-39\) \(q+(2+2\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}+4\zeta_{6}q^{4}+\cdots\)
169.4.e.c \(4\) \(9.971\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) \(q+4\zeta_{12}q^{2}+(-2+2\zeta_{12}^{2})q^{3}+8\zeta_{12}^{2}q^{4}+\cdots\)
169.4.e.d \(4\) \(9.971\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
169.4.e.e \(4\) \(9.971\) \(\Q(\zeta_{12})\) None \(0\) \(14\) \(0\) \(0\) \(q+5\zeta_{12}q^{2}+(7-7\zeta_{12}^{2})q^{3}+17\zeta_{12}^{2}q^{4}+\cdots\)
169.4.e.f \(8\) \(9.971\) 8.0.1731891456.1 None \(0\) \(-10\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{2}-3\beta _{7})q^{3}+(-4-3\beta _{2}+\cdots)q^{4}+\cdots\)
169.4.e.g \(8\) \(9.971\) 8.0.1731891456.1 None \(0\) \(-10\) \(0\) \(0\) \(q+(-\beta _{1}-2\beta _{3}+\beta _{6}-2\beta _{7})q^{2}+(-1+\cdots)q^{3}+\cdots\)
169.4.e.h \(36\) \(9.971\) None \(0\) \(-2\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(169, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(169, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)