Properties

Label 272.10.a
Level $272$
Weight $10$
Character orbit 272.a
Rep. character $\chi_{272}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $12$
Sturm bound $360$
Trace bound $5$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 272.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(360\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(272))\).

Total New Old
Modular forms 330 72 258
Cusp forms 318 72 246
Eisenstein series 12 0 12

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

\(2\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(17\)
\(+\)\(-\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(19\)
\(-\)\(-\)\(+\)\(17\)
Plus space\(+\)\(34\)
Minus space\(-\)\(38\)

Trace form

\( 72q + 162q^{3} - 2750q^{7} + 472392q^{9} + O(q^{10}) \) \( 72q + 162q^{3} - 2750q^{7} + 472392q^{9} + 21986q^{11} + 120972q^{15} - 670140q^{19} + 634168q^{21} + 53942q^{23} + 28887552q^{25} + 10049544q^{27} - 4511232q^{29} - 21158646q^{31} - 2566728q^{33} + 19120308q^{35} - 1214776q^{37} - 35468688q^{39} - 3633992q^{41} + 137083580q^{43} - 13805000q^{45} - 175570560q^{47} + 419740672q^{49} + 40591206q^{51} + 74907848q^{53} - 158432004q^{55} - 141556552q^{57} + 49534260q^{59} - 103676922q^{63} + 119062824q^{65} + 423033072q^{67} + 224559728q^{69} - 441183954q^{71} + 502617600q^{73} - 58649842q^{75} + 93212160q^{77} - 471543298q^{79} + 2825893888q^{81} + 397761580q^{83} + 3395836388q^{87} - 1049140040q^{89} - 2514971976q^{91} + 937580944q^{93} + 774164712q^{95} + 1809005128q^{97} + 346948030q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(272))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 17
272.10.a.a \(2\) \(140.090\) \(\Q(\sqrt{43}) \) None \(0\) \(-64\) \(-2788\) \(728\) \(-\) \(-\) \(q+(-2^{5}+\beta )q^{3}+(-1394-30\beta )q^{5}+\cdots\)
272.10.a.b \(3\) \(140.090\) \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(0\) \(-84\) \(-1304\) \(-690\) \(-\) \(+\) \(q+(-28+\beta _{1})q^{3}+(-435-3\beta _{1}-\beta _{2})q^{5}+\cdots\)
272.10.a.c \(3\) \(140.090\) 3.3.3262740.1 None \(0\) \(-84\) \(1314\) \(-6912\) \(-\) \(-\) \(q+(-28+\beta _{2})q^{3}+(438+13\beta _{1}-4\beta _{2})q^{5}+\cdots\)
272.10.a.d \(4\) \(140.090\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-226\) \(-1656\) \(-2654\) \(-\) \(+\) \(q+(-57-\beta _{1})q^{3}+(-412+4\beta _{1}-3\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.e \(5\) \(140.090\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(236\) \(-1138\) \(-3712\) \(-\) \(-\) \(q+(47-\beta _{1})q^{3}+(-227+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.f \(5\) \(140.090\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(236\) \(1480\) \(13202\) \(-\) \(+\) \(q+(47-\beta _{3})q^{3}+(295-2\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.g \(7\) \(140.090\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-88\) \(1362\) \(-9388\) \(-\) \(-\) \(q+(-13+\beta _{1})q^{3}+(195-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
272.10.a.h \(7\) \(140.090\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(74\) \(1480\) \(-5132\) \(-\) \(+\) \(q+(11-\beta _{1})q^{3}+(212-\beta _{1}-\beta _{4})q^{5}+\cdots\)
272.10.a.i \(8\) \(140.090\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-152\) \(176\) \(-48\) \(+\) \(+\) \(q+(-19+\beta _{1})q^{3}+(22+\beta _{2})q^{5}+(-6+\cdots)q^{7}+\cdots\)
272.10.a.j \(9\) \(140.090\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-10\) \(-176\) \(5952\) \(+\) \(+\) \(q+(-1-\beta _{1})q^{3}+(-19-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.k \(9\) \(140.090\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(314\) \(-1426\) \(10754\) \(+\) \(-\) \(q+(35+\beta _{1})q^{3}+(-158+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
272.10.a.l \(10\) \(140.090\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(10\) \(2676\) \(-4850\) \(+\) \(-\) \(q+(1+\beta _{1})q^{3}+(268+\beta _{2})q^{5}+(-485+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(272))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(272)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)