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Properties

Label 252.12.j
Level $252$
Weight $12$
Character orbit 252.j
Rep. character $\chi_{252}(85,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $132$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 252.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(252, [\chi])\).

Total New Old
Modular forms 1068 132 936
Cusp forms 1044 132 912
Eisenstein series 24 0 24

Trace form

\( 132 q - 1032 q^{3} + 1958 q^{5} + 133876 q^{9} + O(q^{10}) \) \( 132 q - 1032 q^{3} + 1958 q^{5} + 133876 q^{9} - 52580 q^{11} - 16176242 q^{15} + 7412332 q^{17} + 25275372 q^{19} - 12538022 q^{21} + 63777256 q^{23} - 671146344 q^{25} - 282332592 q^{27} - 135001798 q^{29} - 76608906 q^{31} + 231077312 q^{33} + 420175000 q^{35} + 911309916 q^{37} + 1116722716 q^{39} + 976467570 q^{41} - 1354458342 q^{43} + 239112002 q^{45} + 2955581706 q^{47} - 18643366434 q^{49} - 3504975478 q^{51} + 7950777240 q^{53} - 8756664972 q^{55} - 5798375514 q^{57} + 12938217932 q^{59} - 5155849776 q^{63} - 19567620702 q^{65} + 14923947384 q^{67} + 4509813488 q^{69} - 32609359868 q^{71} - 6931731036 q^{73} - 36013464674 q^{75} - 21654273256 q^{77} - 15059325066 q^{79} + 4991545240 q^{81} + 51741266086 q^{83} + 108290140314 q^{85} + 35892390076 q^{87} - 211299069924 q^{89} - 44112929532 q^{91} + 59349724018 q^{93} - 202892578316 q^{95} + 34518800352 q^{97} + 434020416544 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{12}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)