Properties

Label 252.12.k
Level $252$
Weight $12$
Character orbit 252.k
Rep. character $\chi_{252}(37,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $74$
Newform subspaces $5$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 1080 74 1006
Cusp forms 1032 74 958
Eisenstein series 48 0 48

Trace form

\( 74 q - 8781 q^{5} + 10938 q^{7} + O(q^{10}) \) \( 74 q - 8781 q^{5} + 10938 q^{7} + 241251 q^{11} + 342056 q^{13} - 6331947 q^{17} + 14241631 q^{19} + 14475 q^{23} - 343222722 q^{25} - 190045860 q^{29} + 214796057 q^{31} + 263542035 q^{35} - 156900803 q^{37} + 1529728008 q^{41} + 105125476 q^{43} - 460975779 q^{47} + 384023792 q^{49} - 6342914499 q^{53} + 448940774 q^{55} + 1313612865 q^{59} + 3691238411 q^{61} + 22871285340 q^{65} - 6110168319 q^{67} - 7949996172 q^{71} + 6609355365 q^{73} - 12044100873 q^{77} - 81105066217 q^{79} + 236279328852 q^{83} + 56935465382 q^{85} - 47653296015 q^{89} - 115090438858 q^{91} - 209303212953 q^{95} + 86014234068 q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.12.k.a \(2\) \(193.622\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-76885\) \(q+(-25539-25807\zeta_{6})q^{7}-2248615q^{13}+\cdots\)
252.12.k.b \(14\) \(193.622\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(-7218\) \(35001\) \(q+(1031\beta _{1}+\beta _{3})q^{5}+(2668+336\beta _{1}+\cdots)q^{7}+\cdots\)
252.12.k.c \(14\) \(193.622\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(-3719\) \(-83356\) \(q+(-531+531\beta _{1}-\beta _{2}-\beta _{5})q^{5}+\cdots\)
252.12.k.d \(16\) \(193.622\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(2156\) \(50512\) \(q+(269\beta _{1}-\beta _{3})q^{5}+(1064+4186\beta _{1}+\cdots)q^{7}+\cdots\)
252.12.k.e \(28\) \(193.622\) None \(0\) \(0\) \(0\) \(85666\)

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

\( S_{12}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)