Properties

Label 441.2.bb
Level $441$
Weight $2$
Character orbit 441.bb
Rep. character $\chi_{441}(37,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $264$
Newform subspaces $6$
Sturm bound $112$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bb (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 6 \)
Sturm bound: \(112\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(441, [\chi])\).

Total New Old
Modular forms 720 288 432
Cusp forms 624 264 360
Eisenstein series 96 24 72

Trace form

\( 264q + 13q^{2} + 7q^{4} + 16q^{5} - 8q^{7} + 8q^{8} + O(q^{10}) \) \( 264q + 13q^{2} + 7q^{4} + 16q^{5} - 8q^{7} + 8q^{8} - 18q^{10} + 23q^{11} - 2q^{13} - 19q^{14} + 9q^{16} + 21q^{17} + 15q^{19} + 34q^{20} - 16q^{22} - 7q^{23} - 2q^{25} + 26q^{26} - 72q^{28} - 28q^{29} + 37q^{31} + 61q^{32} - 42q^{34} + 26q^{35} - 61q^{37} - 30q^{38} + 14q^{40} - 34q^{41} - 34q^{43} - 34q^{44} - 98q^{46} - 29q^{47} + 44q^{49} + 148q^{50} + 114q^{52} - 51q^{53} + 13q^{55} - 140q^{56} + 72q^{58} + 12q^{59} + 45q^{61} + 8q^{62} + 32q^{64} + 16q^{65} + q^{67} - 77q^{68} - 82q^{70} + 41q^{71} - 3q^{73} + 28q^{74} + 3q^{76} + 27q^{77} - 7q^{79} - 120q^{80} - 174q^{82} - 58q^{83} - 74q^{85} - 51q^{86} - 137q^{88} - 72q^{89} - 142q^{91} - 46q^{92} - 222q^{94} - 125q^{95} - 16q^{97} - 185q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
441.2.bb.a \(12\) \(3.521\) \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(q+(2-2\zeta_{21}^{2}+2\zeta_{21}^{3}-2\zeta_{21}^{5}+2\zeta_{21}^{6}+\cdots)q^{4}+\cdots\)
441.2.bb.b \(24\) \(3.521\) None \(0\) \(0\) \(0\) \(28\)
441.2.bb.c \(48\) \(3.521\) None \(1\) \(0\) \(0\) \(0\)
441.2.bb.d \(48\) \(3.521\) None \(13\) \(0\) \(14\) \(-14\)
441.2.bb.e \(60\) \(3.521\) None \(-1\) \(0\) \(2\) \(5\)
441.2.bb.f \(72\) \(3.521\) None \(0\) \(0\) \(0\) \(-28\)

Decomposition of \(S_{2}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)